Cornered Heegaard Floer homology

TL;DR

This paper extends bordered Floer homology to 3-manifolds with codimension-2 corners, enabling the computation of their invariants through tensor products of cornered invariants, thus broadening the scope of Floer homology techniques.

Contribution

It introduces cornered Floer homology invariants for 3-manifolds with corners and proves they can be combined via tensor products to recover the invariants of the whole manifold.

Findings

Construction of cornered Floer homology invariants

Tensor product formula for manifolds with corners

Extension of bordered Floer homology framework

Abstract

Bordered Floer homology assigns invariants to 3-manifolds with boundary, such that the Heegaard Floer homology of a closed 3-manifold, split into two pieces, can be recovered as a tensor product of the bordered invariants of the pieces. We construct cornered Floer homology invariants of 3-manifolds with codimension-2 corners, and prove that the bordered Floer homology of a 3-manifold with boundary, split into two pieces with corners, can be recovered as a tensor product of the cornered invariants of the pieces.