On the algebra of cornered Floer homology

On the Algebra of Cornered Floer Homology

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...

Lectures on Floer homology

On the Floer homology of cotangent bundles

This paper concerns Floer homology for periodic orbits and for a Lagrangian intersection problem on the cotangent bundle T M of a compact orientable manifold M . The first result is a new L estimate for the solutions of the Floer equation, which allows to deal with a larger and more natural class of Hamiltonians. The second and main result is a new construction of the isomorphism between the Fl...

On combinatorial link Floer homology

Link Floer homology is an invariant for links defined using a suitable version of Lagrangian Floer homology. In an earlier paper, this invariant was given a combinatorial description with mod 2 coefficients. In the present paper, we give a self-contained presentation of the basic properties of link Floer homology, including an elementary proof of its invariance. We also fix signs for the differ...

Floer Homology on the Extended Moduli Space

Given a Heegaard splitting of a 3-manifold, we use Lagrangian Floer homology to construct a relatively Z/8Z-graded abelian group, which we conjecture to be a 3-manifold invariant. Our motivation is to have a well-defined symplectic side of the Atiyah-Floer Conjecture, for arbitrary 3-manifolds. The symplectic manifold used in the construction is the extended moduli space of flat SU(2)-connectio...