arXiv:1806.09391 Abstract | arXiv Analytics

arXiv:1806.09391 [math.GT]Abstract References Reviews Resources

Locality and the Uniqueness of Quantum Invariants

Published 2018-06-25Version 1

We introduce the notion of a "state function" for framed tangles in a disk. After choosing a finite set of states for each marked disk, a state function is a projection from the vector space spanned by all tangles to the vector space spanned by the states, that is local, and topologically invariant. Given the states for the Kauffman bracket, and the quantum $SU(3)$-invariant we classify all state functions, and then compare our results to the literature.

Comments: 23 pages, 46 figures

Categories: math.GT

Subjects: 57M27

Keywords: quantum invariants, state function, uniqueness, vector space, kauffman bracket

Related articles: Most relevant | Search more

arXiv:1101.2695 [math.GT] (Published 2011-01-13)

Dubois' Torsion, A-polynomial and Quantum Invariants

Charles Frohman, Joanna Kania-Bartoszynska

arXiv:math/0210011 [math.GT] (Published 2002-10-01)

Quantum invariants of Seifert 3-manifolds and their asymptotic expansions

Soren Kold Hansen, Toshie Takata

arXiv:2010.05890 [math.GT] (Published 2020-10-12)