A TQFT for Wormhole cobordisms over the field of rational functions

Patrick Gilmer

Banach Center Publications (1998)

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

Abstract

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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 ( π i ) / ( 2 r ) . We relate our work to Hoste and Przytycki’s calculation of the Kauffman bracket skein module of S 1 × S 2 .

How to cite

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Gilmer, 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 -

References

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