Skip to main content
Search type Search syntax
Tags [tag]
Exact "words here"
Author user:1234
user:me (yours)
Score score:3 (3+)
score:0 (none)
Answers answers:3 (3+)
answers:0 (none)
isaccepted:yes
hasaccepted:no
inquestion:1234
Views views:250
Code code:"if (foo != bar)"
Sections title:apples
body:"apples oranges"
URL url:"*.example.com"
Saves in:saves
Status closed:yes
duplicate:no
migrated:no
wiki:no
Types is:question
is:answer
Exclude -[tag]
-apples
For more details on advanced search visit our help page
Results tagged with
Search options answers only not deleted user 2356

Hamiltonian systems, symplectic flows, classical integrable systems

2 votes

Why we have to fix markers in SFT?

I'll talk about cylindrical contact homology, which is a relatively well-established part of SFT. It's a variant of Hamiltonian Floer homology for contact manifolds. Let α be a contact 1-form …
Tim Perutz's user avatar
  • 13.2k
3 votes

SFT compactness

For non-specialist readers: SFT = symplectic field theory BEHWZ = Bourgeois-Eliashberg-Hofer-Wysocki-Zehnder, the authors of the paper which establishes the basic compactness theorem for pseudo-hol …
Tim Perutz's user avatar
  • 13.2k
14 votes
Accepted

Kuranishi structures vs polyfolds

Kuranishi models are a traditional - and beautiful - technique for describing the local structure of moduli spaces cut out by non-linear equations whose linearization is Fredholm. A more elaborate ver …
Tim Perutz's user avatar
  • 13.2k
11 votes
Accepted

Orientations for pseudoholomorphic curves with totally real boundary condition

1) The problem of orienting moduli spaces of pseudo-holomorphic discs with totally real boundary conditions is really a problem in index theory. It was solved Vin de Silva in his (unpublished) D. Phil …
Tim Perutz's user avatar
  • 13.2k
3 votes
Accepted

Homotopy classes of complex bundle maps and isotropic immersions into contact manifolds

jc, you'll have fun working out answers to examples of your first question. I'm only going to address the Legendrian case. If I didn't make mistakes, I'll conclude that Legendrian immersions of Sn
Tim Perutz's user avatar
  • 13.2k
6 votes
Accepted

A Poisson Geometry Version of the Fukaya Category

The fundamental technique of symplectic topology is the theory of pseudo-holomorphic curves. One studies maps u from a Riemann surface into a symplectic manifold, equipped with an almost complex str …
Tim Perutz's user avatar
  • 13.2k
7 votes

Hamiltonian circle actions and Lefschetz pencils

Hm, good question. This would be potentially interesting from the point of view of classifying Hamiltonian circle-actions, "by induction" on the dimension. (1) I'm pretty sure that the answer is not …
Tim Perutz's user avatar
  • 13.2k
6 votes
Accepted

The higher structure of the Floer cochains of the diagonal in CP^ x CP^n

Here's an argument that the diagonal Lagrangian correspondence Δ in CPn×CPn is formal. That is, its Floer cochains CF(Δ,Δ), as an A-algebr …
Tim Perutz's user avatar
  • 13.2k
24 votes
Accepted

What is the Poincare dual of a symplectic form?

One of the big advances in symplectic topology in the 90s was Donaldson's theorem that when the symplectic class is integral, high multiples of its dual are represented by symplectic submanifolds. T …
Tim Perutz's user avatar
  • 13.2k
6 votes

Are there symplectic 4-folds with b+>1, b=0?

Symplectic geography in 4 dimensions can be mapped using Chern number coordinates (c21,c2). The part of the plane where c21>4c2 is uncharted. It's unknown whether there are any symplectic …
Tim Perutz's user avatar
  • 13.2k
11 votes
Accepted

symplectic 4-manifolds with free circle action

Here's an example, using a construction of Fernandez, Gray and Morgan (1991): Take a closed surface S with area form ω, let ϕ be an area-preserving diffeomorphism, and $p\colon S_\phi …
Tim Perutz's user avatar
  • 13.2k
11 votes

Real interpretations of Discontinuities in Floer homology

The brief answer is yes, using ideas from Novikov homology. Here's an example of the discontinuity and how it can be fixed. Take L=S1×y as a Lagrangian in standard symplectic $T^2=S^1\time …
Tim Perutz's user avatar
  • 13.2k
20 votes

When are two symplectic forms "isotopic"?

There is a cheap way to find cohomologous but non-isotopic (in fact, non-deformation equivalent) symplectic forms: start with a symplectic manifold and pull back the symplectic form via a diffeomorphi …
Tim Perutz's user avatar
  • 13.2k
8 votes
Accepted

Length of Floer flow lines

In your symplectically aspherical setting, bounds on length will indeed exist. Suppose one has a sequence of solutions un to Floer's equation, of bounded energy, and a sequence of points $t_n\in …
Tim Perutz's user avatar
  • 13.2k
14 votes
Accepted

Obstruction bundle for spaces with Kuranishi structure

Here's a view of the symplectic side of the bridge. The Kuranishi model (see Donaldson-Kronheimer, The geometry of four-manifolds, ch. 4) goes like this. You're interested in a (moduli) space M cut …
Tim Perutz's user avatar
  • 13.2k

15 30 50 per page