dorsal/arxiv
View SchemaThe space of 3-manifolds and Vassiliev finite-type invariants
| Authors | Nadya Shirokova |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9705008 |
| URL | https://arxiv.org/abs/q-alg/9705008 |
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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"abstract": "In this paper we develop the theory of finite-type invariants for\nhomologically nontrivial 3-manifolds. We construct an infinite-dimensional\naffine space with a hypersurface in it corresponding to manifolds with Morse\nsingularities. Connected components of the complement of this hypersurface\ncorrespond to homeomorphism type of spin 3-manifolds. This suggests the natural\naxiomatics of Vassiliev finite-type invariants for arbitrary closed\n3-manifolds. An example of an invariant of order 1 is given.",
"arxiv_id": "q-alg/9705008",
"authors": [
"Nadya Shirokova"
],
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"title": "The space of 3-manifolds and Vassiliev finite-type invariants",
"url": "https://arxiv.org/abs/q-alg/9705008"
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