Volume 10, issue 3 (2010)

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Remarks on $2$–dimensional HQFTs

Mihai D Staic and Vladimir Turaev

Algebraic & Geometric Topology 10 (2010) 1367–1393
Abstract

We introduce and study algebraic structures underlying 2–dimensional Homotopy Quantum Field Theories (HQFTs) with arbitrary target spaces. These algebraic structures are formalized in the notion of a twisted Frobenius algebra. Our work generalizes results of Brightwell, Turner and the second author on 2–dimensional HQFTs with simply connected or aspherical targets.

Keywords
topological quantum field theory, Frobenius algebra, $k$–invariant
Mathematical Subject Classification 2000
Primary: 57R56
References
Publication
Received: 14 December 2009
Revised: 30 March 2010
Accepted: 4 May 2010
Published: 17 June 2010
Authors
Mihai D Staic
Department of Mathematics
Indiana University
Rawles Hall
Bloomington IN 47405
United States
Institute of Mathematics of the Romanian Academy
PO Box 1-764
RO-70700 Bucharest
Romania
Vladimir Turaev
Department of Mathematics
Indiana University
Rawles Hall
Bloomington IN 47405
United States