A TQFT for Wormhole cobordisms over the field of rational functions

Gilmer, Patrick

Gilmer, Patrick

Banach Center Publications, Tome 43 (1998), p. 119-127 / Harvested from The Polish Digital Mathematics Library

Résumé

We consider a cobordism category whose morphisms are punctured connected 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 rth Witten-Reshetikhin-Turaev invariant of a link in some wormhole space, properly normalized, is the value of a certain rational function at $e^{(π i) / (2 r)}$ . We relate our work to Hoste and Przytycki’s calculation of the Kauffman bracket skein module of $S^{1} \times S^{2}$ .

Publié le : 1998-01-01

Zbl 0907.57004

EUDML-ID : urn:eudml:doc:208799

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     author = {Gilmer, Patrick},
     title = {A TQFT for Wormhole cobordisms over the field of rational functions},
     journal = {Banach Center Publications},
     volume = {43},
     year = {1998},
     pages = {119-127},
     zbl = {0907.57004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv42i1p119bwm}
}

Gilmer, Patrick. A TQFT for Wormhole cobordisms over the field of rational functions. Banach Center Publications, Tome 43 (1998) pp. 119-127. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv42i1p119bwm/

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