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On the unification of quantum 3-manifold invariants


Beliakova, A; Le, T (2011). On the unification of quantum 3-manifold invariants. In: Jablan, S; Kauffmann, H; Lambropoulou, S; Przytycki, H. Introductory lectures on knot theory. Selected lectures presented at the advanced school and conference on knot theory and its applications to physics and biology, ICTP, Trieste, Italy, May 11--29, 2009. New Jersey: World Scientific, 1-21.

Abstract

In 2006 Habiro initiated a construction of generating functions for Witten–Reshetikhin–Turaev (WRT) invariants known as unified WRT invariants. In a series of papers together with Irmgard Bühler and Christian Blanchet we extended his construction to a larger class of 3–manifolds. The unified invariants provide a strong tool to study properties of the whole collection of WRT invariants, e.g. their integrality, and hence, their categorification. In this paper we give a survey on ideas and techniques used in the construction of the unified invariants.

Abstract

In 2006 Habiro initiated a construction of generating functions for Witten–Reshetikhin–Turaev (WRT) invariants known as unified WRT invariants. In a series of papers together with Irmgard Bühler and Christian Blanchet we extended his construction to a larger class of 3–manifolds. The unified invariants provide a strong tool to study properties of the whole collection of WRT invariants, e.g. their integrality, and hence, their categorification. In this paper we give a survey on ideas and techniques used in the construction of the unified invariants.

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Additional indexing

Item Type:Book Section, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2011
Deposited On:09 Jan 2013 14:47
Last Modified:05 Apr 2016 16:18
Publisher:World Scientific
Number:46
ISBN:978-981-4307-99-4 (P) 978-981-4313-00-1 (E)
Publisher DOI:https://doi.org/10.1142/9789814313001_0001

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