A note on the involutive invariants of splices

Abstract

A natural family of potentially 2-torsion elements in the integer homology cobordism group consists of splices of knots with their mirrors. We show that such 3-manifolds have locally trivial involutive Floer homology. We show some related families of splices also have locally trivial involutive Floer homology. Our arguments show that many gauge theoretic invariants also vanish on these 3-manifolds.

15 pages. v2: Typo corrections and minor clarifications. This version to be published in Algebraic & Geometric Topology