The space of 3-manifolds

Authors
Citation
N. Shirokova, The space of 3-manifolds, CR AC S I, 331(2), 2000, pp. 131-136
Citations number
4
Categorie Soggetti
Mathematics
Journal title
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE
ISSN journal
07644442 → ACNP
Volume
331
Issue
2
Year of publication
2000
Pages
131 - 136
Database
ISI
SICI code
0764-4442(20000715)331:2<131:TSO3>2.0.ZU;2-4
Abstract
In this paper we develop the theory of finite-type invariants for homologic ally nontrivial 3-manifolds. We construct an infinite-dimensional Euclidean space with a hypersurface in it corresponding to manifolds with Morse sing ularities. The connected components of the complement to the discriminant c orrespond to homeomorphism classes of spin 3-manifolds. We give the definit ion of the invariant of finite type, suggested by the geometry of the space and give an example or the invariant of order 1. (C) 2000 Academie des sci ences/Editions scientifiques et medicales Elsevier SAS.