Geodesic
Remarks on 2–dimensional HQFTs
Staic, Mihai D1 ; Turaev, Vladimir2
1Department 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
2Department of Mathematics, Indiana University, Rawles Hall, Bloomington IN 47405, United States
Algebraic and Geometric Topology, Tome 10 (2010) no. 3, pp. 1367-1393
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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.

DOI : 10.2140/agt.2010.10.1367
Keywords: topological quantum field theory, Frobenius algebra, $k$–invariant

Staic, Mihai D  1   ; Turaev, Vladimir  2

1 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
2 Department of Mathematics, Indiana University, Rawles Hall, Bloomington IN 47405, United States 
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Staic, Mihai D; Turaev, Vladimir. Remarks on 2–dimensional HQFTs. Algebraic and Geometric Topology, Tome 10 (2010) no. 3, pp. 1367-1393. doi: 10.2140/agt.2010.10.1367

[1] M Atiyah, Topological quantum field theories, Inst. Hautes Études Sci. Publ. Math. (1988)

[2] M Brightwell, P Turner, Representations of the homotopy surface category of a simply connected space, J. Knot Theory Ramifications 9 (2000) 855

[3] S Eilenberg, S Maclane, Determination of the second homology and cohomology groups of a space by means of homotopy invariants, Proc. Nat. Acad. Sci. U. S. A. 32 (1946) 277

[4] T Porter, V Turaev, Formal homotopy quantum field theories. I. Formal maps and crossed C–algebras, J. Homotopy Relat. Struct. 3 (2008) 113

[5] V Turaev, Homotopy field theory in dimension 2 and group-algebras

[6] V Turaev, Homotopy Quantum Field Theory, 10, European Math. Soc. (2010)

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