Cobordism category of plumbed 3-manifolds and intersection product structures

Details Cobordism category of plumbed 3-manifolds and intersection product structures Cobordism category of plumbed 3-manifolds and intersection product structures

2009-01-26

arxiv.org/abs/0901.3941v1

Mathematics

Geometric Topology

25 pages

Scientific paper

In this paper, we introduce a category of graded commutative rings with certain algebraic morphisms, to investigate the cobordism category of plumbed 3-manifolds. In particular, we define a non-associative distributive algebra that gives necessary conditions for an abstract morphism between the homologies of two plumbed 3-manifolds to be realized geometrically by a cobordism. Here we also consider the homology cobordism monoid, and give a necessary condition using w-invariants for the homology 3-spheres to belong to the inertia group associated to some homology 3-spheres.

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