Skeins, SU( N ) three-manifold invariants and TQFT | Zendy

W. B. R. Lickorish | Zendy

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Skeins, SU( N ) three-manifold invariants and TQFT

Author(s) -

W. B. R. Lickorish

Publication year - 2000

Publication title -

commentarii mathematici helvetici

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.603

H-Index - 46

eISSN - 1420-8946

pISSN - 0010-2571

DOI - 10.1007/s000140050112

Subject(s) - topological quantum field theory , mathematics , skein , bracket polynomial , skein relation , homfly polynomial , pure mathematics , jones polynomial , finite type invariant , knot theory , invariant (physics) , torus , manifold (fluid mechanics) , algebra over a field , polynomial , invariant polynomial , mathematical analysis , knot (papermaking) , mathematical physics , geometry , mechanical engineering , alternating polynomial , matrix polynomial , chemical engineering , square free polynomial , engineering

The skein theory associated to the HOMFLY polynomial invariant of oriented knots and links in the three-sphere is explored in order to provide the background results necessary for the creation of a Topological Quantum Field Theory. A simple local duality result in the skein theory is proved. It allows vector space dimensions in the theory to be correlated with the structure constants in a skein algebra associated to the solid torus.

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