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2003 HKR-type invariants of 4–thickenings of 2–dimensional CW complexes
Ivelina Bobtcheva, Maria Grazia Messia
Algebr. Geom. Topol. 3(1): 33-87 (2003). DOI: 10.2140/agt.2003.3.33

Abstract

The HKR (Hennings–Kauffman–Radford) framework is used to construct invariants of 4–thickenings of 2–dimensional CW complexes under 2–deformations (1– and 2– handle slides and creations and cancellations of 1–2 handle pairs). The input of the invariant is a finite dimensional unimodular ribbon Hopf algebra A and an element in a quotient of its center, which determines a trace function on A. We study the subset T4 of trace elements which define invariants of 4–thickenings under 2–deformations. In T4 two subsets are identified : T3T4, which produces invariants of 4–thickenings normalizable to invariants of the boundary, and T2T4, which produces invariants of 4–thickenings depending only on the 2–dimensional spine and the second Whitney number of the 4–thickening. The case of the quantum sl(2) is studied in details. We conjecture that sl(2) leads to four HKR–type invariants and describe the corresponding trace elements. Moreover, the fusion algebra of the semisimple quotient of the category of representations of the quantum sl(2) is identified as a subalgebra of a quotient of its center.

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Ivelina Bobtcheva. Maria Grazia Messia. "HKR-type invariants of 4–thickenings of 2–dimensional CW complexes." Algebr. Geom. Topol. 3 (1) 33 - 87, 2003. https://doi.org/10.2140/agt.2003.3.33

Information

Received: 22 July 2002; Revised: 27 November 2002; Accepted: 10 January 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1031.57019
MathSciNet: MR1997313
Digital Object Identifier: 10.2140/agt.2003.3.33

Subjects:
Primary: 57N13
Secondary: 16W30, 57M20, 57N10

Rights: Copyright © 2003 Mathematical Sciences Publishers

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