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Oct
12 |
awarded | Yearling |
Apr
18 |
awarded | Civic Duty |
Oct
22 |
comment |
Dimension of moduli space in Lagrangian Floer homology
Let me add two more references - Appendix C of McDuff and Salamon's big book explains why the index of the operator on the disc obtained by capping off the Hamiltonian orbit end of the half cylinder is given by the Maslov index of the Lagrangian loop $u^*T\Lambda$ (wrt the chosen trivialization) - and Matthias Schwarz' thesis has a very detailed proof (see Section 3.3) as to why the index of the operator on the cap is given by the CZ index. Since the index is additive, as Sam says the index on the half cylinder is [index of capped cylinder] - [index of cap], which gives the required answer. |
Oct
15 |
comment |
why $H_{1}(\Sigma)\cong H_{1}(Sym^{g}(\Sigma))$ ?
This question is answered here: math.stackexchange.com/questions/45923/… |
Aug
19 |
awarded | Yearling |
Aug
15 |
awarded | Good Answer |
May
24 |
comment |
Length of Floer flow lines
This question was actually asked on my behalf, so thanks Tim for your answer (and apologies for the delay). Let me also add an answer of my own: in the non-compact case (which is what we were primarily interested in), the existence of such length bounds seems to be essentially equivalent to the existence of $L^{\infty}$ bounds on gradient flows lines. One direction uses Tim's answer - as once $L^{\infty}$ bounds are established one can invoke Gromov compactness as in the closed case. The converse can be made explicit at least in the case of quadratic Hamiltonians on cotangent bundles, say. |
May
24 |
revised |
Splitting of the double tangent bundle into vertical and horizontal parts, and defining partial derivatives
Fixed error |
Apr
18 |
comment |
What's the difference between 2 and 3?
All the prime numbers less than or equal to 2 are even, and all the prime numbers greater than or equal to 3 are odd :) |
Apr
6 |
awarded | Disciplined |
Apr
6 |
revised |
Splitting of the double tangent bundle into vertical and horizontal parts, and defining partial derivatives
added 253 characters in body |
Apr
6 |
answered | Splitting of the double tangent bundle into vertical and horizontal parts, and defining partial derivatives |
Apr
6 |
awarded | Nice Answer |
Feb
15 |
answered | A $C^2$ small autonomous Hamiltonian has only constant 1-periodic orbits |
Feb
12 |
awarded | Fanatic |
Jan
24 |
awarded | Nice Answer |
Jan
24 |
comment |
Books you would like to read (if somebody would just write them…)
I should say that very recently such a book has been written by Audin and Damian - "Théorie de Morse et homologie de Floer", which is a beautiful and comprehensive introduction to the easiest parts of Floer homology. My only complaint with this book is that it doesn't go quite far enough - I guess I'm thinking more of a book the size of McDuff and Salamon's wonderful "J-holomorphic curves and symplectic topology" - but written specifically for Floer theory. |
Jan
24 |
answered | Books you would like to read (if somebody would just write them…) |
Dec
27 |
awarded | Critic |
Dec
27 |
answered | Why does the group act on the right on the principal bundle? |