A trivial tail homology for non $A$-adequate links

TL;DR

This paper proves that Rozansky's tail homology groups are trivial for non $A$-adequate links, confirming a conjecture and clarifying the behavior of tail homology in link categorification.

Contribution

It establishes that Rozansky's tail homology is trivial for non $A$-adequate links, confirming a conjecture and advancing understanding of link categorification.

Findings

Tail homology groups are trivial for non $A$-adequate links

Confirmed Rozansky's conjecture on tail homology behavior

Clarified the distinction between $A$-adequate and non $A$-adequate links

Abstract

We prove a conjecture of Rozansky's concerning his categorification of the tail of the colored Jones polynomial for an $A$-adequate link. We show that the tail homology groups he constructs are trivial for non $A$-adequate links.