dorsal/arxiv
View SchemaA TQFT for Wormhole cobordisms over the field of rational functions
| Authors | Patrick Gilmer |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9507015 |
| URL | https://arxiv.org/abs/q-alg/9507015 |
| Journal | Knot Theory, Warsaw 1995 ,ed V.F.R.Jones , J.Kania-Bartoszynska , J.H.Przytycki , P.Traczyk ,V.Turaev, Banach Center Publications 42,1998, 119-127 |
Abstract
We consider a cobordism category whose morphisms are punctured connect sums of $S^1 \times S^2$'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 $r$th Witten-Reshetikhin-Turaev invariant of a link in some wormhole space, properly normalized, is the value of a certain rational function at $e^{\frac{\pi i}{2r}}.$ We relate our work to Hoste and Przytycki's calculation of the Kauffman bracket skein module of $S^1 \times S^2.$
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"abstract": "We consider a cobordism category whose morphisms are punctured connect sums\nof $S^1 \\times S^2$\u0027s (wormhole spaces) with embedded admissibly colored banded\ntrivalent graphs. We define a TQFT on this cobordism category over the field of\nrational functions in an indeterminant $A.$ For $r$ large, we recover, by\nspecializing $A$ to a primitive 4rth root of unity, the\nWitten-Reshetikhin-Turaev TQFT restricted to links in wormhole spaces. Thus,\nfor $r$ large, the $r$th Witten-Reshetikhin-Turaev invariant of a link in some\nwormhole space, properly normalized, is the value of a certain rational\nfunction at $e^{\\frac{\\pi i}{2r}}.$ We relate our work to Hoste and Przytycki\u0027s\ncalculation of the Kauffman bracket skein module of $S^1 \\times S^2.$",
"arxiv_id": "q-alg/9507015",
"authors": [
"Patrick Gilmer"
],
"categories": [
"q-alg",
"math.QA"
],
"journal_ref": "Knot Theory, Warsaw 1995 ,ed V.F.R.Jones , J.Kania-Bartoszynska ,\n J.H.Przytycki , P.Traczyk ,V.Turaev, Banach Center Publications 42,1998,\n 119-127",
"title": "A TQFT for Wormhole cobordisms over the field of rational functions",
"url": "https://arxiv.org/abs/q-alg/9507015"
},
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