# Quantum Enhancements of Involutory Birack Counting Invariants

@article{Nelson2012QuantumEO, title={Quantum Enhancements of Involutory Birack Counting Invariants}, author={Sam Nelson and Veronica Rivera}, journal={arXiv: Geometric Topology}, year={2012} }

The involutory birack counting invariant is an integer-valued invariant of unoriented tangles defined by counting homomorphisms from the fundamental involutory birack of the tangle to a finite involutory birack over a set of framings modulo the birack rank of the labeling birack. In this first of an anticipated series of several papers, we enhance the involutory birack counting invariant with quantum weights, which may be understood as tangle functors of involutory birack-labeled unoriented…

## 7 Citations

Quantum Enhancements and Biquandle Brackets

- Mathematics
- 2015

We introduce a new class of quantum enhancements we call biquandle brackets, which are customized skein invariants for biquandle colored links.Quantum enhancements of biquandle counting invariants…

Biquandle virtual brackets

- MathematicsJournal of Knot Theory and Its Ramifications
- 2019

We introduce an infinite family of quantum enhancements of the biquandle counting invariant which we call biquandle virtual brackets. Defined in terms of skein invariants of biquandle colored…

Quantum Enhancements via Tribracket Brackets

- PhysicsMediterranean Journal of Mathematics
- 2020

We enhance the tribracket counting invariant with \textit{tribracket brackets}, skein invariants of tribracket-colored oriented knots and links analogously to biquandle brackets. This infinite family…

A Survey of Quantum Enhancements

- MathematicsKnots, Low-Dimensional Topology and Applications
- 2019

In this short survey article we collect the current state of the art in the nascent field of \textit{quantum enhancements}, a type of knot invariant defined by collecting values of quantum invariants…

Picture-valued parity-biquandle bracket II. Examples.

- Mathematics
- 2019

In [3] we constructed the parity-biquandle bracket valued in {\em pictures} (linear combinations of $4$-valent graphs). We gave no example of classical links such that the parity-biquandle bracket of…

Picture-valued parity-biquandle bracket

- Mathematics
- 2020

In V. O. Manturov, On free knots, preprint (2009), arXiv:math.GT/0901.2214], the second named author constructed the bracket invariant [⋅] of virtual knots valued in pictures (linear combinations o...

Picture-valued biquandle bracket

- Mathematics
- 2017

In [14], the second named author constructed the bracket invariant [.] of virtual knots valued in pictures (linear combinations of virtual knot diagrams with some crossing information omitted), such…

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