The space of 3-manifolds and Vassiliev finite-type invariants

Details The space of 3-manifolds and Vassiliev finite-type invariants The space of 3-manifolds and Vassiliev finite-type invariants

1997-05-09

arxiv.org/abs/q-alg/9705008v2

Mathematics

Quantum Algebra

9 pages, plain TEX

Scientific paper

In this paper we develop the theory of finite-type invariants for homologically nontrivial 3-manifolds. We construct an infinite-dimensional affine space with a hypersurface in it corresponding to manifolds with Morse singularities. Connected components of the complement of this hypersurface correspond to homeomorphism type of spin 3-manifolds. This suggests the natural axiomatics of Vassiliev finite-type invariants for arbitrary closed 3-manifolds. An example of an invariant of order 1 is given.

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