On the algebra of cornered Floer homology
Geometric Topology
2017-01-23 v4 Algebraic Topology
Quantum Algebra
Symplectic Geometry
Abstract
Bordered Floer homology associates to a parametrized oriented surface a certain differential graded algebra. We study the properties of this algebra under splittings of the surface. To the circle we associate a differential graded 2-algebra, the nilCoxeter sequential 2-algebra, and to a surface with connected boundary an algebra-module over this 2-algebra, such that a natural gluing property is satisfied. Moreover, with a view toward the structure of a potential Floer homology theory of 3-manifolds with codimension-two corners, we present a decomposition theorem for the Floer complex of a planar grid diagram, with respect to vertical and horizontal slicing.
Keywords
Cite
@article{arxiv.1105.0113,
title = {On the algebra of cornered Floer homology},
author = {Christopher L. Douglas and Ciprian Manolescu},
journal= {arXiv preprint arXiv:1105.0113},
year = {2017}
}
Comments
a few minor revisions