Back to Papers Home
Back to Papers of School of Mathematics
|
Paper
IPM / M / 16150 |
School of Mathematics
|
|
Title: |
A refinement of sutured Floer homology
|
|
Author(s): |
Eaman Eftekhary (Joint with A. Alishahi)
|
|
Status: |
Published
|
|
Journal: |
J. Symplectic Geom.
|
|
Vol.: |
13
|
|
Year: |
2015
|
|
Pages: |
609-743
|
|
Supported by: |
IPM
|
|
|
Abstract: |
We introduce a refinement of the Ozsváth-Szabó complex
associated to a balanced sutured manifold (X,τ) by Juhász [].
An algebra \Ringτ is associated to the boundary of a sutured manifold and
a filtration of its generators by \Ht2(X,∂X;\Z) is defined.
For a fixed class \spinc of a \SpinC structure over the manifold
\ovl X, which is obtained from X by filling out the sutures,
the Ozsváth-Szabó chain complex \CFT(X,τ,\spinc)
is then defined as a chain complex with coefficients in \Ringτ and
filtered by \SpinC(X,τ). The filtered chain homotopy type
of this chain complex is an invariant of (X,τ) and the
\SpinC class \spinc ∈ \SpinC(\ovl X). The construction
generalizes the construction of Juhász. It plays the role of
\CFT−(X,\spinc) when X is a closed three-manifold, and
the role of
|
\CFKT−(Y,K;\spinc)= |
⊕
\relspinc ∈ \spinc
|
\CFKT−(Y,K,\relspinc), |
|
when the sutured manifold is obtained from a knot K inside a three-manifold Y.
Our invariants generalize both the knot invariants of
Ozsváth-Szabó and Rasmussen and the link invariants of Ozsváth and Szabó.
We study some of the basic properties of the corresponding Ozsváth-Szabó
complex, including the exact triangles, and some form of stabilization.
Download TeX format
|
|
back to top
|
