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Spherical 2-Categories and 4-Manifold Invariants

✍ Scribed by Marco Mackaay

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 472 KB
Volume: 143
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.1998.1798

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✦ Synopsis

Definition 1.4. Let V(M, T, l) be the tensor product of the state spaces of all the tetrahedra of T in which the ordering of the factors is as described above. The tensor product of the respective partition functions applied to V(M, T, l) has its image in a permuted tensor product V(M, T, l)$. Again Remark 1.1 is vital. Now compose this linear map with the linear map P(M, T, l): V(M, T, l)$ Ä V(M, T, l) induced by the standard transposition P : x y Ä y x. The result is a linear map L(M, T, l) : V(M, T, l) Ä V(M, T, l). The element Z(M, T, l) # F is defined to be the trace of L(M, T, l).

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