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

1997/05/09 by Nadya Shirokova, Shirokova, Nadya
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9705008

9 pages, plain TEX

openalex publication_date 1997/05/09 · arxiv created 1997/05/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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