A quantum obstruction to embedding

Frohman, Charles; Kania-Bartoszynska, Joanna

doi:10.1017/s0305004101005230

Cited by 13 publications

(5 citation statements)

References 16 publications

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“…For other oriented surfaces, A 1 (F, ∅, R) is isomorphic to the Kauffman bracket skein module of F × I, [HP2,P5,P6,PS]. (For more on Kauffman bracket skein modules see [Bu1,Bu2,BFK1,BFK2,BHMV,BP,FG,FGL,FK,GS1,GS2,GH,HP3,HP4,Le,Sa1,Sa2,S1,S3,Tu].) Consequently, Corollary 4.1 immediately implies the result of Przytycki, [P6, Theorem 3.1]: Theorem 9.4.…”

Section: Partition Category and Dichromatic Reduction Rulesmentioning

confidence: 72%

Confluence theory for graphs

Sikora

Westbury

2007

Algebr. Geom. Topol.

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We develop a theory of confluence of graphs. We describe an algorithm for proving that a given system of reduction rules for abstract graphs and graphs in surfaces is locally confluent. We apply this algorithm to show that each simple Lie algebra of rank at most 2, gives rise to a confluent system of reduction rules of graphs (via Kuperberg's spiders) in an arbitrary surface. As a further consequence of this result, we find canonical bases of S U 3 -skein modules of cylinders over orientable surfaces.57M15, 57M27; 05C10, 16S15

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Section: Partition Category and Dichromatic Reduction Rulesmentioning

confidence: 72%

Confluence theory for graphs

Sikora

Westbury

2007

Algebr. Geom. Topol.

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“…Remark 3.6. Recall J + p (N ), the Frohman Kania-Bartoszynska ideal [FKB,GM1,G2] of a compact connected oriented 3-manifold N with connected boundary Σ. Using our orthogonal basis, we can give generators for this ideal as follows.…”

Section: Orthogonal Lollipop Basis In Higher Genusmentioning

confidence: 99%

Integral topological quantum field theory for a one-holed torus

Gilmer¹,

Masbaum²

2011

Pacific J. Math.

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We give new explicit formulas for the representations of the mapping class group of a genus-one surface with one boundary component which arise from integral TQFT. Our formulas allow the straightforward computation of the h-adic expansion of the TQFT-matrix associated to a mapping class. Truncating the h-adic expansion gives an approximation of the representation by representations into finite groups. As a special case, we study the induced representations over finite fields and identify them up to isomorphism. The key technical ingredient of the paper are new bases of the integral TQFT modules which are orthogonal with respect to the Hopf pairing. We construct these orthogonal bases in arbitrary genus, and briefly describe some other applications of them.

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“…The s i form an orthonormal basis with respect to (9). This pairing identifies the linear dual of K t (A) with series of the form i α i s i , where the α i are complex numbers.…”

Section: The Yang-mills Measure On a Closed Surfacementioning

confidence: 99%

“…The quotient is denoted K r,f (M ). The reduced skein K r,f (M ) is a central object in the construction of quantum invariants of 3-manifolds [9,22,23].…”

Section: Roots Of Unitymentioning

confidence: 99%