Advanced Differential Geometry Textbook
$begingroup$
In algebraic topology there are two canonical "advanced" textbooks that go quite far beyond the usual graduate courses.
They are Switzer Algebraic Topology: Homology and Homotopy and Whitehead Elements of Homotopy Theory. These are both excellent books that (theoretically) give you overviews and introduction to most of the main topics that you need for becoming a modern researcher in algebraic topology.
Differential Geometry seems replete with excellent introductory textbooks. From Lee to do Carmo to so many others.
Now you might be thinking that Kobayashi/Nomizu seems natural. But the age of those books is showing in terms of what people are really doing today compared to what you learn from using those books. They just aren't the most efficient way to learn modern differential geometry (or so I've heard).
I am looking for a book that covers topics like Characteristic Classes, Index Theory, the analytic side of manifold theory, Lie groups, Hodge theory, Kahler manifolds and complex geometry, symplectic and Poisson geometry, Riemmanian Geometry and geometric analysis, and perhaps some relations to algebraic geometry and mathematical physics. But none of these topics completely, just as Switzer does with a unifying perspective and proofs of legitimate results done at an advanced level, but really as an introduction to each of the topics (Switzer does this with K-theory, spectral sequences, cohomology operations, Spectra...).
The only book I have found that is sort of along these lines is Nicolaescu's Lectures on the Geometry of Manifolds, but this book misses many topics.
This was inspired by page viii of Lee's excellent book: link
where he lists some of these other topics and almost implies that they would take another volume. I'm wondering whether that advanced volume exists.
Any recommendations for great textbooks/monographs would be much appreciated!
differential-geometry reference-request manifolds riemannian-geometry book-recommendation
edited Jan 27 '18 at 8:43
Martin Sleziak
44.8k9118272
asked Aug 23 '15 at 22:03
DiffGeomInterestDiffGeomInterest
491
$endgroup$
add a comment |
$begingroup$
In algebraic topology there are two canonical "advanced" textbooks that go quite far beyond the usual graduate courses.
They are Switzer Algebraic Topology: Homology and Homotopy and Whitehead Elements of Homotopy Theory. These are both excellent books that (theoretically) give you overviews and introduction to most of the main topics that you need for becoming a modern researcher in algebraic topology.
Differential Geometry seems replete with excellent introductory textbooks. From Lee to do Carmo to so many others.
Now you might be thinking that Kobayashi/Nomizu seems natural. But the age of those books is showing in terms of what people are really doing today compared to what you learn from using those books. They just aren't the most efficient way to learn modern differential geometry (or so I've heard).
I am looking for a book that covers topics like Characteristic Classes, Index Theory, the analytic side of manifold theory, Lie groups, Hodge theory, Kahler manifolds and complex geometry, symplectic and Poisson geometry, Riemmanian Geometry and geometric analysis, and perhaps some relations to algebraic geometry and mathematical physics. But none of these topics completely, just as Switzer does with a unifying perspective and proofs of legitimate results done at an advanced level, but really as an introduction to each of the topics (Switzer does this with K-theory, spectral sequences, cohomology operations, Spectra...).
The only book I have found that is sort of along these lines is Nicolaescu's Lectures on the Geometry of Manifolds, but this book misses many topics.
This was inspired by page viii of Lee's excellent book: link
where he lists some of these other topics and almost implies that they would take another volume. I'm wondering whether that advanced volume exists.
Any recommendations for great textbooks/monographs would be much appreciated!
differential-geometry reference-request manifolds riemannian-geometry book-recommendation
edited Jan 27 '18 at 8:43
Martin Sleziak
44.8k9118272
asked Aug 23 '15 at 22:03
DiffGeomInterestDiffGeomInterest
491
$endgroup$
2
$begingroup$
I like this book editions-ellipses.fr/product_info.php?products_id=7505 . Of course, it does not cover all these topics. And I think such book would not exist since each one of these topics are connected in many different ways (it would contain say 5000 pages at least). You may like amazon.com/Differentiable-Manifolds-Yozo-Matsushima/dp/… too. By the way, Kobayashi and Nomizu still a good book (and is not out of date).
$endgroup$
– user40276
Aug 24 '15 at 1:45
$begingroup$
The question is now posted also on MathOverflow: Advanced Differential Geometry Textbook
$endgroup$
– Martin Sleziak
Jan 27 '18 at 8:43
$begingroup$
Are you aware of KMS's Natural operations in differential geometry?
$endgroup$
– Jackozee Hakkiuz
Jan 4 at 5:30
add a comment |
$begingroup$
In algebraic topology there are two canonical "advanced" textbooks that go quite far beyond the usual graduate courses.
They are Switzer Algebraic Topology: Homology and Homotopy and Whitehead Elements of Homotopy Theory. These are both excellent books that (theoretically) give you overviews and introduction to most of the main topics that you need for becoming a modern researcher in algebraic topology.
Differential Geometry seems replete with excellent introductory textbooks. From Lee to do Carmo to so many others.
Now you might be thinking that Kobayashi/Nomizu seems natural. But the age of those books is showing in terms of what people are really doing today compared to what you learn from using those books. They just aren't the most efficient way to learn modern differential geometry (or so I've heard).
I am looking for a book that covers topics like Characteristic Classes, Index Theory, the analytic side of manifold theory, Lie groups, Hodge theory, Kahler manifolds and complex geometry, symplectic and Poisson geometry, Riemmanian Geometry and geometric analysis, and perhaps some relations to algebraic geometry and mathematical physics. But none of these topics completely, just as Switzer does with a unifying perspective and proofs of legitimate results done at an advanced level, but really as an introduction to each of the topics (Switzer does this with K-theory, spectral sequences, cohomology operations, Spectra...).
The only book I have found that is sort of along these lines is Nicolaescu's Lectures on the Geometry of Manifolds, but this book misses many topics.
This was inspired by page viii of Lee's excellent book: link
where he lists some of these other topics and almost implies that they would take another volume. I'm wondering whether that advanced volume exists.
Any recommendations for great textbooks/monographs would be much appreciated!
differential-geometry reference-request manifolds riemannian-geometry book-recommendation
edited Jan 27 '18 at 8:43
Martin Sleziak
44.8k9118272
asked Aug 23 '15 at 22:03
DiffGeomInterestDiffGeomInterest
491
$endgroup$
In algebraic topology there are two canonical "advanced" textbooks that go quite far beyond the usual graduate courses.
They are Switzer Algebraic Topology: Homology and Homotopy and Whitehead Elements of Homotopy Theory. These are both excellent books that (theoretically) give you overviews and introduction to most of the main topics that you need for becoming a modern researcher in algebraic topology.
Differential Geometry seems replete with excellent introductory textbooks. From Lee to do Carmo to so many others.
Now you might be thinking that Kobayashi/Nomizu seems natural. But the age of those books is showing in terms of what people are really doing today compared to what you learn from using those books. They just aren't the most efficient way to learn modern differential geometry (or so I've heard).
I am looking for a book that covers topics like Characteristic Classes, Index Theory, the analytic side of manifold theory, Lie groups, Hodge theory, Kahler manifolds and complex geometry, symplectic and Poisson geometry, Riemmanian Geometry and geometric analysis, and perhaps some relations to algebraic geometry and mathematical physics. But none of these topics completely, just as Switzer does with a unifying perspective and proofs of legitimate results done at an advanced level, but really as an introduction to each of the topics (Switzer does this with K-theory, spectral sequences, cohomology operations, Spectra...).
The only book I have found that is sort of along these lines is Nicolaescu's Lectures on the Geometry of Manifolds, but this book misses many topics.
This was inspired by page viii of Lee's excellent book: link
where he lists some of these other topics and almost implies that they would take another volume. I'm wondering whether that advanced volume exists.
Any recommendations for great textbooks/monographs would be much appreciated!
differential-geometry reference-request manifolds riemannian-geometry book-recommendation
differential-geometry reference-request manifolds riemannian-geometry book-recommendation
edited Jan 27 '18 at 8:43
Martin Sleziak
44.8k9118272
asked Aug 23 '15 at 22:03
DiffGeomInterestDiffGeomInterest
491
edited Jan 27 '18 at 8:43
Martin Sleziak
44.8k9118272
asked Aug 23 '15 at 22:03
DiffGeomInterestDiffGeomInterest
491
edited Jan 27 '18 at 8:43
Martin Sleziak
44.8k9118272
edited Jan 27 '18 at 8:43
Martin Sleziak
44.8k9118272
edited Jan 27 '18 at 8:43
Martin Sleziak
44.8k9118272
44.8k9118272
asked Aug 23 '15 at 22:03
DiffGeomInterestDiffGeomInterest
491
asked Aug 23 '15 at 22:03
DiffGeomInterestDiffGeomInterest
491
asked Aug 23 '15 at 22:03
DiffGeomInterestDiffGeomInterest
491
491
2
$begingroup$
I like this book editions-ellipses.fr/product_info.php?products_id=7505 . Of course, it does not cover all these topics. And I think such book would not exist since each one of these topics are connected in many different ways (it would contain say 5000 pages at least). You may like amazon.com/Differentiable-Manifolds-Yozo-Matsushima/dp/… too. By the way, Kobayashi and Nomizu still a good book (and is not out of date).
$endgroup$
– user40276
Aug 24 '15 at 1:45
$begingroup$
The question is now posted also on MathOverflow: Advanced Differential Geometry Textbook
$endgroup$
– Martin Sleziak
Jan 27 '18 at 8:43
$begingroup$
Are you aware of KMS's Natural operations in differential geometry?
$endgroup$
– Jackozee Hakkiuz
Jan 4 at 5:30
add a comment |
2
$begingroup$
I like this book editions-ellipses.fr/product_info.php?products_id=7505 . Of course, it does not cover all these topics. And I think such book would not exist since each one of these topics are connected in many different ways (it would contain say 5000 pages at least). You may like amazon.com/Differentiable-Manifolds-Yozo-Matsushima/dp/… too. By the way, Kobayashi and Nomizu still a good book (and is not out of date).
$endgroup$
– user40276
Aug 24 '15 at 1:45
$begingroup$
The question is now posted also on MathOverflow: Advanced Differential Geometry Textbook
$endgroup$
– Martin Sleziak
Jan 27 '18 at 8:43
$begingroup$
Are you aware of KMS's Natural operations in differential geometry?
$endgroup$
– Jackozee Hakkiuz
Jan 4 at 5:30
2
2
$begingroup$
I like this book editions-ellipses.fr/product_info.php?products_id=7505 . Of course, it does not cover all these topics. And I think such book would not exist since each one of these topics are connected in many different ways (it would contain say 5000 pages at least). You may like amazon.com/Differentiable-Manifolds-Yozo-Matsushima/dp/… too. By the way, Kobayashi and Nomizu still a good book (and is not out of date).
$endgroup$
– user40276
Aug 24 '15 at 1:45
$begingroup$
I like this book editions-ellipses.fr/product_info.php?products_id=7505 . Of course, it does not cover all these topics. And I think such book would not exist since each one of these topics are connected in many different ways (it would contain say 5000 pages at least). You may like amazon.com/Differentiable-Manifolds-Yozo-Matsushima/dp/… too. By the way, Kobayashi and Nomizu still a good book (and is not out of date).
$endgroup$
– user40276
Aug 24 '15 at 1:45
$begingroup$
The question is now posted also on MathOverflow: Advanced Differential Geometry Textbook
$endgroup$
– Martin Sleziak
Jan 27 '18 at 8:43
$begingroup$
The question is now posted also on MathOverflow: Advanced Differential Geometry Textbook
$endgroup$
– Martin Sleziak
Jan 27 '18 at 8:43
$begingroup$
Are you aware of KMS's Natural operations in differential geometry?
$endgroup$
– Jackozee Hakkiuz
Jan 4 at 5:30
$begingroup$
Are you aware of KMS's Natural operations in differential geometry?
$endgroup$
– Jackozee Hakkiuz
Jan 4 at 5:30
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Of course this is not the book that you are looking for, since it covers only one topic, but thoroughly and it is a classic :
MILNOR -STASHEFF "Characteristic Classes"
A nice and complete book on Complex Geometry is that of WELLS - GARCIA PRADA. "Differential Analysis on Complex Manifolds", where you may find Complex Characteristic Classes (Chern Classes), and Hodge theory, besides Elliptic Operators.
answered Nov 23 '18 at 18:56
vanmerivanmeri
658
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add a comment |
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$begingroup$
Of course this is not the book that you are looking for, since it covers only one topic, but thoroughly and it is a classic :
MILNOR -STASHEFF "Characteristic Classes"
A nice and complete book on Complex Geometry is that of WELLS - GARCIA PRADA. "Differential Analysis on Complex Manifolds", where you may find Complex Characteristic Classes (Chern Classes), and Hodge theory, besides Elliptic Operators.
answered Nov 23 '18 at 18:56
vanmerivanmeri
658
$endgroup$
add a comment |
$begingroup$
Of course this is not the book that you are looking for, since it covers only one topic, but thoroughly and it is a classic :
MILNOR -STASHEFF "Characteristic Classes"
A nice and complete book on Complex Geometry is that of WELLS - GARCIA PRADA. "Differential Analysis on Complex Manifolds", where you may find Complex Characteristic Classes (Chern Classes), and Hodge theory, besides Elliptic Operators.
answered Nov 23 '18 at 18:56
vanmerivanmeri
658
$endgroup$
add a comment |
$begingroup$
Of course this is not the book that you are looking for, since it covers only one topic, but thoroughly and it is a classic :
MILNOR -STASHEFF "Characteristic Classes"
A nice and complete book on Complex Geometry is that of WELLS - GARCIA PRADA. "Differential Analysis on Complex Manifolds", where you may find Complex Characteristic Classes (Chern Classes), and Hodge theory, besides Elliptic Operators.
answered Nov 23 '18 at 18:56
vanmerivanmeri
658
$endgroup$
Of course this is not the book that you are looking for, since it covers only one topic, but thoroughly and it is a classic :
MILNOR -STASHEFF "Characteristic Classes"
A nice and complete book on Complex Geometry is that of WELLS - GARCIA PRADA. "Differential Analysis on Complex Manifolds", where you may find Complex Characteristic Classes (Chern Classes), and Hodge theory, besides Elliptic Operators.
answered Nov 23 '18 at 18:56
vanmerivanmeri
658
answered Nov 23 '18 at 18:56
vanmerivanmeri
658
answered Nov 23 '18 at 18:56
vanmerivanmeri
658
answered Nov 23 '18 at 18:56
vanmerivanmeri
658
658
add a comment |
add a comment |
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$begingroup$
I like this book editions-ellipses.fr/product_info.php?products_id=7505 . Of course, it does not cover all these topics. And I think such book would not exist since each one of these topics are connected in many different ways (it would contain say 5000 pages at least). You may like amazon.com/Differentiable-Manifolds-Yozo-Matsushima/dp/… too. By the way, Kobayashi and Nomizu still a good book (and is not out of date).
$endgroup$
– user40276
Aug 24 '15 at 1:45
$begingroup$
The question is now posted also on MathOverflow: Advanced Differential Geometry Textbook
$endgroup$
– Martin Sleziak
Jan 27 '18 at 8:43
$begingroup$
Are you aware of KMS's Natural operations in differential geometry?
$endgroup$
– Jackozee Hakkiuz
Jan 4 at 5:30