A signature invariant for knotted Klein graphs

TL;DR

This paper introduces signature invariants for knotted trivalent graphs using branched covers, relating them to classical knot signatures and demonstrating their computation on a specific example.

Contribution

It defines new signature invariants for knotted Klein graphs and connects them to classical signatures, providing a method for their computation.

Findings

Signature invariants for knotted Klein graphs are established.

The invariants are related to classical knot and link signatures.

An explicit computation is demonstrated on Kinoshita's knotted theta graph.

Abstract

We define some signature invariants for a class of knotted trivalent graphs using branched covers. We relate them to classical signatures of knots and links. Finally, we explain how to compute these invariants through the example of Kinoshita's knotted theta graph.