Relation between quantum invariants of 3-manifolds and 2-dimensional CW-complexes

Details Relation between quantum invariants of 3-manifolds and 2-dimensional CW-complexes Relation between quantum invariants of 3-manifolds and 2-dimensional CW-complexes

2000-12-21

arxiv.org/abs/math/0012212v1

Mathematics

Geometric Topology

16 pages, Latex

Scientific paper

We show that the Reshetikhin-Turaev-Walker invariant of 3-manifolds can be normalized to obtain an invariant of 4-dimensional thickenings of 2-complexes. Moreover when the underlying semisimple tortile category comes from the representations of a quantum group at a primitive prime root of unity, the 0-term in the Ohtsuki expansion of this invariant depends only on the spine and is the mod p invariant of 2-complexes defined previously from the second author. As a consequence it is shown that when the Euler characteristic is greater or equal to 1, the 2-complex invariant depends only on homology. The last statement doesn't hold for the negative Euler characteristic case.

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