Zobrazeno 1 - 10
of 24
pro vyhledávání: '"57K31, 57K16"'
Autor:
Wang, Sike, Wong, Helen
The Kauffman bracket skein algebra of a surface is a generalization of the Jones polynomial invariant for links and plays a principal role in the Witten-Reshetikhin- Turaev topological quantum field theory. However, the multiplicative structure of th
Externí odkaz:
http://arxiv.org/abs/2405.20159
We show that the Kauffman bracket skein module of a closed Seifert fibered 3-manifold $M$ is finitely generated over $\mathbb Z[A^{\pm 1}]$ if and only if $M$ is irreducible and non-Haken. We analyze in detail the character varieties $X(M)$ of such m
Externí odkaz:
http://arxiv.org/abs/2405.18557
In this paper, we investigate residual finiteness and subquandle separability of quandles. The existence of these finiteness properties implies the solvability of the word problem and the generalised word problem for quandles. We prove that the funda
Externí odkaz:
http://arxiv.org/abs/2403.17703
Autor:
Murakami, Jun, van der Veen, Roland
The theory of bottom tangles is used to construct a quantum fundamental group. On the other hand, the skein module is considered as a quantum analogue of the $SL(2)$ representation of the fundamental group. Here we construct the skein module of a kno
Externí odkaz:
http://arxiv.org/abs/2402.06891
Autor:
Sozer, Kursat, Virelizier, Alexis
This is an invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics. We give an overview of 3-dimensional topological quantum field theories (TQFTs) and the corresponding quantum invariants of 3-manifolds. We recall the mai
Externí odkaz:
http://arxiv.org/abs/2401.10587
The proof of Witten's finiteness conjecture established that the Kauffman bracket skein modules of closed $3$-manifolds are finitely generated over $\mathbb Q(A)$. In this paper, we develop a novel method for computing these skein modules. We show th
Externí odkaz:
http://arxiv.org/abs/2305.16188
Chromatic maps for spherical tensor categories are instrumental tools to construct (non semisimple) invariants of 3-manifolds and their extension to (non compact) (2+1)-TQFTs. In this paper, we introduce left and right chromatic maps for finite tenso
Externí odkaz:
http://arxiv.org/abs/2305.14626
Autor:
Korablev, Philipp
In the paper we introduce the construction of invariants for 3-manifolds, based on the same key concepts as the classical Dijkgraaf-Witten invariant. We introduce the notion of a special $G$-system and describe how each system induces the invariant n
Externí odkaz:
http://arxiv.org/abs/2305.00737
Autor:
Kinnear, Patrick
We determine the dimension of the Kauffman bracket skein module at generic $q$ for mapping tori of the 2-torus, generalising the well-known computation of Carrega and Gilmer. In the process, we give a decomposition of the twisted Hochschild homology
Externí odkaz:
http://arxiv.org/abs/2304.07332
Autor:
Kaiser, Uwe
The author defined for each (commutative) Frobenius algebra a skein module of surfaces in a $3$-manifold $M$ bounding a closed $1$-manifold $\alpha \subset \partial M$. The surface components are colored by elements of the Frobenius algebra. The modu
Externí odkaz:
http://arxiv.org/abs/2211.01937