...
Subcritical
...
manifolds
...
and
...
algebraic
...
structures
...
In
...
the
...
morning
...
we
...
will
...
go
...
through
...
the
...
computation
...
of
...
symplectic
...
cohomology
...
for
...
affine
...
space.
...
Using
...
Cieliebak's
...
result
...
that
...
subcritical
...
Weinstein
...
manifolds
...
split,
...
we'll
...
obtain
...
a
...
computation
...
for
...
this
...
class
...
of
...
manifolds.
...
Wiki Markup Compute the symplectic cohomology of
...
the ball following the outline in Section (3f) of \[Seidel\]. The easiest way to do this is to follow the second approach, and compute the Conley-Zehnder index of the unique time-1 Hamiltonian orbit of the function t\|r\|^2 when t is not a multiple of 2pi.
...
Wiki Markup Introduce the notion of a Weinstein manifold, and that of a subcritical Weinstein manifold. Explain Cieliebak's splitting result for subcritical manifolds (see Theorem 14.16 of \[Cieliebak-Eliashberg\]).
...
Wiki Markup Explain the statement of the main result of \[Oancea-K\]. Use this to compute symplectic cohomology for subcritical Weinstein manifolds.
...
In
...
the
...
afternoon,
...
we
...
will
...
discuss
...
algebraic
...
structures
...
on
...
symplectic
...
cohomology.
...
Wiki Markup The product on symplectic cohomology is defined by counting pairs of pants. Explain the proof of associativity, and the construction of the unit. The construction of these operations is outlined in Section (8a) of \[Seidel\], which \[Ritter\] elaborates upon.
...
- Define
...
- the
...
- BV
...
- operator,
...
- and
...
- use
...
- it,
...
- and
...
- its
...
- higher
...
- analogues,
...
- to
...
- define
...
- S^1
...
- equivariant
...
- symplectic
...
- cohomology.
...
- Introduce
...
- contact
...
- homology,
...
- and
...
- outline
...
- the
...
- construction
...
- of
...
- an
...
- isomorphism
...
- between
...
- S^1
...
- equivariant
...
- symplectic
...
- cohomology
...
- and
...
- contact
...
- homology.