# A TQFT for Wormhole cobordisms over the field of rational functions

Banach Center Publications (1998)

- Volume: 42, Issue: 1, page 119-127
- ISSN: 0137-6934

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topGilmer, Patrick. "A TQFT for Wormhole cobordisms over the field of rational functions." Banach Center Publications 42.1 (1998): 119-127. <http://eudml.org/doc/208799>.

@article{Gilmer1998,

abstract = {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 $S^1 × S^2$.},

author = {Gilmer, Patrick},

journal = {Banach Center Publications},

keywords = {Kauffman bracket; fusion rules},

language = {eng},

number = {1},

pages = {119-127},

title = {A TQFT for Wormhole cobordisms over the field of rational functions},

url = {http://eudml.org/doc/208799},

volume = {42},

year = {1998},

}

TY - JOUR

AU - Gilmer, Patrick

TI - A TQFT for Wormhole cobordisms over the field of rational functions

JO - Banach Center Publications

PY - 1998

VL - 42

IS - 1

SP - 119

EP - 127

AB - 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 $S^1 × S^2$.

LA - eng

KW - Kauffman bracket; fusion rules

UR - http://eudml.org/doc/208799

ER -

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