Bordered Floer homology with integral coefficients for manifolds with torus boundary

TL;DR

This paper develops a combinatorial bordered Floer homology theory with integer coefficients for 3-manifolds with torus boundary, aligning with existing combinatorial Heegaard Floer homology.

Contribution

It introduces a new combinatorial framework for bordered Floer homology with integral coefficients, extending previous theories.

Findings

Provides a combinatorial definition of bordered Floer theory with Z coefficients.

Recovers the combinatorial Heegaard Floer homology for manifolds with torus boundary.

Establishes a foundation for further computational and theoretical work in Floer homology.

Abstract

We provide a combinatorial definition of a bordered Floer theory with $\mathbb Z$ coefficients for manifolds with torus boundary. Our bordered Floer structures recover the combinatorial Heegaard Floer homology defined by Ozsv\'ath, Stipsicz, and Szab\'o.