A New Perspective for an Existing Homology Theory of Links Embedded in I-Bundles

TL;DR

This paper presents a novel homology theory for links in I-bundles over orientable surfaces, where chain groups are surfaces, and demonstrates its equivalence to a known homology theory.

Contribution

It introduces a surface-based homology theory for links in I-bundles and proves its equivalence to an existing homology framework.

Findings

The new theory uses surfaces as chain group elements.

It yields the same results as the Asaeda-Przytycki-Sikora homology.

The approach offers a different perspective on link homology.

Abstract

This paper introduces a homology theory for links in I-bundles over an orientable surface. The theory is unique in that the elements of the chain groups are surfaces instead of diagrams. It is then shown this theory yields the same results as the homology theory constructed by Asaeda, Przytycki and Sikora.