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1998 | 42 | 1 | 119-127
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A TQFT for Wormhole cobordisms over the field of rational functions

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We consider a cobordism category whose morphisms are punctured connected sums of $S^1 × S^2$'s (wormhole spaces) with embedded admissibly colored banded trivalent graphs. We define a TQFT on this cobordism category over the field of rational functions in an indeterminant A. For r large, we recover, by specializing A to a primitive 4rth root of unity, the Witten-Reshetikhin-Turaev TQFT restricted to links in wormhole spaces. Thus, for r large, the rth Witten-Reshetikhin-Turaev invariant of a link in some wormhole space, properly normalized, is the value of a certain rational function at $e^{(πi)/(2r)}$. We relate our work to Hoste and Przytycki's calculation of the Kauffman bracket skein module of $S^1 × S^2$.
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  • Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803, U.S.A.
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