An introduction to tangle Floer homology

TL;DR

This paper introduces the combinatorial framework of tangle Floer homology, detailing two equivalent definitions and providing explicit computations to facilitate understanding and application in low-dimensional topology.

Contribution

It presents a comprehensive introduction to the combinatorial tangle Floer homology, including two equivalent definitions and explicit computational examples.

Findings

Two equivalent combinatorial definitions of tangle Floer homology

Explicit computations demonstrating the theory

Discussion of the correspondence between definitions

Abstract

This paper is a short introduction to the combinatorial version of tangle Floer homology defined in "Combinatorial tangle Floer homology". There are two equivalent definitions---one in terms of strand diagrams, and one in terms of bordered grid diagrams. We present both, discuss the correspondence, and carry out some explicit computations.