3-Manifold group and finite decomposition complexity
نویسندگان
چکیده
منابع مشابه
On Finite Type 3-manifold Invariants Iii: Manifold Weight Systems
The present paper is a continuation of [Oh2] and [GL] devoted to the study of finite type invariants of integral homology 3-spheres. We introduce the notion of manifold weight systems, and show that type m invariants of integral homology 3-spheres are determined (modulo invariants of type m − 1) by their associated manifold weight systems. In particular we deduce a vanishing theorem for finite ...
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We define an invariant, which we call surface-complexity, of closed 3manifolds by means of Dehn surfaces. The surface-complexity of a manifold is a natural number measuring how much the manifold is complicated. We prove that it fulfils interesting properties: it is subadditive under connected sum and finite-to-one on P-irreducible manifolds. Moreover, for P-irreducible manifolds, it equals the ...
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The purpose of the present paper is, among other things, to relate the seemingly unrelated notions of surgical equivalence of links in S 3 ((Le1]) and the notion of nite type invariants of oriented integral homology 3-spheres, due to T. Ohtsuki Oh]. The paper consists of two parts. In the rst part we classify pure braids and string links modulo the relation of surgical equivalence. We prove tha...
متن کاملOn Finite Type 3-manifold Invariants I
Recently Ohtsuki Oh2], motivated by the notion of nite type knot invariants, introduced the notion of nite type invariants for oriented, integral ho-mology 3-spheres (ZHS for short). In the present paper we propose another definition of nite type invariants of Z HS and give equivalent reformulations of our notion. We show that our invariants form a ltered commutative algebra and are of nite typ...
متن کاملFinite Type 3-manifold Invariants and the Structure of the Torelli Group I
Using the recently developed theory of finite type invariants of integral homology 3-spheres we study the structure of the Torelli group of a closed surface. Explicitly, we construct (a) natural cocycles of the Torelli group (with coefficients in a space of trivalent graphs) and cohomology classes of the abelianized Torelli group; (b) group homomorphisms that detect (rationally) the nontriviali...
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2010
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2010.01.020