#ADVANCED GEOMETRY FORMULAS PLUS#

Definitely advanced, despite the 1975 date. This is on the boundary between textbook and monograph. Cheeger/Ebin, 'Comparison theorems in Riemannian geometry' (1975).Quite advanced, although not too difficult, despite the 1964 date.

$advanced geometry formulas$

Bishop/Crittenden, 'Geometry of manifolds' (1964).

(These are in chronological order of first editions.) Anyway, these are my suggestions for DG books which are on the boundary between 'textbook' and 'advanced'. A really advanced DG book is typically a monograph because advanced books are at the research level, which is very specialized. By definition, a textbook is what you read to reach an advanced level. There's a kind of a contradiction between 'advanced' and 'textbook'. However most of the articles are research level articles and lack the coherence and unified vision of a textbook/monograph.Ĭoncerning advanced differential geometry textbooks in general: The second volume on complex geometry from the 1989 Proceedings to the In toto, with one obvious exception the geometry of complex manifolds.Thus the reader seeking a complete view of geometry would do well to add Greene and Yau say: 'It is our hope that the three volumes of these proceedings, taken as a whole, will provide a broad overview of geometry and its relationship to mathematics One other reference that I found which people may find interesting is the following: link and link2 where Prof.

#ADVANCED GEOMETRY FORMULAS PLUS#

I'm wondering whether that advanced volume exists.Īny recommendations for great textbooks/monographs would be much appreciated!Įdit: there are many excellent recommendations (I particularly like the Index theory text mentioned by Gordon Craig in the comments as it doesn't shy away from analysis, and does so many things in geometry plus has extensive references) below. 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. 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. 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.). 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. They just aren't the most efficient way to learn modern differential geometry (or so I've heard).

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. Now you might be thinking that Kobayashi/Nomizu seems natural. 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.ĭifferential Geometry seems replete with excellent introductory textbooks. They are Switzer Algebraic Topology: Homology and Homotopy and Whitehead Elements of Homotopy Theory. In algebraic topology there are two canonical 'advanced' textbooks that go quite far beyond the usual graduate courses. Hopefully the experts at MathOverflow can help. I tried this post on StackExchange with no luck.

Advanced geometry formulas