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Allen

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Name Allen
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Jun
7
comment One question on first Stiefel-Whitney class
Thanks Will. As we know, $w_{1}(L)$ goes to the first Chern class of the complexfication of $L$ under the above Bockstein homomorphism. My original motivation is when $c_{1}(L_{\mathbb{C}})=0$ implies $w_{1}(L)=0$.
Jun
7
awarded  Editor
Jun
7
revised One question on first Stiefel-Whitney class
added 8 characters in body
Jun
7
asked One question on first Stiefel-Whitney class
Jun
6
comment One question on cup product and torsion elements
Thanks Allen. Your example is really helpful.
Jun
6
awarded  Scholar
Jun
6
comment One question on cup product and torsion elements
Thanks Tyler, I really appreciate your answer.
Jun
6
comment One question on cup product and torsion elements
Sorry, I always mean nonzero torsion element here.
Jun
6
asked One question on cup product and torsion elements
May
8
awarded  Commentator
May
8
comment Classification of higher dimensional manifolds
Thanks for your reminding, Danny. I always mean classification up to homeomorphism instead of diffeomorphism.
May
7
comment Classification of higher dimensional manifolds
Hi,Scott. You mean his book: Algebraic and Geometric Surgery ?
May
7
comment Classification of higher dimensional manifolds
Ryan, I found a good ref called "A guide to the classication of manifolds" by M. Kreck. It indicates the 3-connected closed 8-manifold already could be quite complicated. You can google "surveys on surgery theory" and the first PDF contains this paper.
May
6
comment Classification of higher dimensional manifolds
Thanks Danny. I have tried Wall's paper. But it seems not that clear to me. Meanwhile the paper did not give a classification when n is even, I suspect.
May
6
comment Classification of higher dimensional manifolds
Not yet. Thanks for the comments.
May
6
asked Classification of higher dimensional manifolds
Jan
5
asked About the MacMahon functions on dimensions bigger than Three
Dec
31
comment (geometric/intuitive) interpretation of ext
The first ext group of two modules(sheaves) can be explictly understood as the set of elements which fit with the given two modules into a short exact sequence (ref. Griffith Harris). For higher ext we have similar construction by going to a diagram of short exact sequences.
Dec
31
comment Example of special Lagrangian fibration of compact CY3?
Mark Gross is an expert in this field. By the way, as far as I know consturcting a special Lag submanifold on a compact CY3 is too difficult, not to say you want a special Lag fibration. This is the reason why many people now only consider Lag fibration for the purpose of mirror symmetry.
Dec
31
asked Universal family of Hibert shemes of Points