manifolds and cobordisms
cobordism theory, Introduction
Definitions
Genera and invariants
Classification
Theorems
Smooth branched -manifolds are a generalization of smooth manifolds which may have ill-defined tangent spaces at certain “branch loci”, where however they are required to have a well defined tangent -plane.
Branched -manifolds arise for instance as quotients of foliations.
1) a collection of closed subsets of
2) for each a finite collection of closed subsets of
3). for each a map to a closed -disk of class in
a) and
b) is a homeomorphism onto its image which is a closed n-disk relative to .
c) There is a “cocycle” of diffeomorphisms of class such that when defined. The domain of is .
Then is called branched n-manifold of class .
This appears as Williams, def. 1.0 ns.
If satisfies this set of axioms with b) replaced by
is a homeomorphisms onto
is called nonsingular branched -manifold of class .
Discussion relating to orbifolds is in
Last revised on February 13, 2013 at 13:06:36. See the history of this page for a list of all contributions to it.