Topological quantum field theory with corners based on the Kauffman bracket

Abstract

Abstract. We describe the construction of a topological quantum field theory with corners based on the Kauffman bracket, that underlies the smooth theory of Lickorish, Blanchet, Habegger, Masbaum and Vogel. We also exhibit some properties of invariants of 3-manifolds with boundary.Mathematics Subject Classification (1991). 57M25, 57N10.

Quantum Computation and the Localization of Modular Functors

“…It is an important observation of Walker's (personal communication) and Gelca's [9] that this description can be extended to labeled surfaces with boundary. (Verification follows directly from the gluing axiom.)…”

Skein modules and the noncommutative torus

“…The idea that they could be used to quantize algebras of functions on surfaces is due to Turaev [19]. They were then used as a tool for constructing quantum invariants by Lickorish [11], Kauffman and Lins [10], Blanchet, Habegger, Masbaum, and Vogel [1], Roberts [16] and Gelca [7]. Finally, the connection between skein modules and characters of the fundamental group of the underlying manifold was explained by Bullock [2], Przytycki and Sikora [14] and Sikora [18].…”

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A quantum obstruction to embedding

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