Birack Bracket Quivers and Framed Links
Sam Nelson, Haoqi Tom Tang
TL;DR
This paper introduces birack brackets as new skein invariants for framed classical and virtual knots, categorifies them into quiver-valued invariants, and derives novel polynomial invariants, advancing knot theory tools.
Contribution
It presents the first birack bracket invariants, categorifies them into quiver invariants, and develops new polynomial invariants for framed knots and links.
Findings
Birack brackets are effective skein invariants for framed knots.
Categorification leads to quiver-valued invariants.
New polynomial invariants are derived from the quiver structures.
Abstract
We introduce birack brackets, skein invariants of birack-colored framed classical and virtual knots and links with values in a commutative unital ring. The multiset of birack bracket values over the homset from a framed link's fundamental birack then forms an invariant of framed links. We then categorify this multiset to define a quiver-valued invariant of framed knots and links. From this quiver we define new polynomial invariants of framed knots and links.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics