Homology of relative trisection and its application

TL;DR

This paper extends the homological analysis of closed 4-manifolds to those with boundary using trisection diagrams and demonstrates how to compute the second Stiefel-Whitney class in this context.

Contribution

It confirms that homology and intersection forms of bordered 4-manifolds can be calculated via relative trisection diagrams, and describes a method to represent the second Stiefel-Whitney class.

Findings

Homology of bordered 4-manifolds can be derived from relative trisection diagrams.

Intersection forms are computable similarly to closed manifolds.

A representative of the second Stiefel-Whitney class is provided.

Abstract

Feller, Klug, Schirmer and Zemke showed the homology and the intersection form of a closed trisected 4-manifold are described in terms of trisection diagram. In this paper, it is confirmed that we are able to calculate those of a trisected 4-manifold with boundary in a similar way. Moreover, we describe a representative of the second Stiefel-Whitney class by the relative trisection diagram.