Mathematics – Geometric Topology
Scientific paper
2009-03-10
Algebr. Geom. Topol. 6 (2006) 539-572
Mathematics
Geometric Topology
This is the version published by Algebraic & Geometric Topology on 7 April 2006
Scientific paper
10.2140/agt.2006.6.539
We give a new and simple proof for the computation of the oriented and the unoriented fold cobordism groups of Morse functions on surfaces. We also compute similar cobordism groups of Morse functions based on simple stable maps of 3-manifolds into the plane. Furthermore, we show that certain cohomology classes associated with the universal complexes of singular fibers give complete invariants for all these cobordism groups. We also discuss invariants derived from hypercohomologies of the universal homology complexes of singular fibers. Finally, as an application of the theory of universal complexes of singular fibers, we show that for generic smooth map germs g: (R^3, 0) --> (R^2, 0) with R^2 being oriented, the algebraic number of cusps appearing in a stable perturbation of g is a local topological invariant of g.
No associations
LandOfFree
Cobordism of Morse functions on surfaces, the universal complex of singular fibers and their application to map germs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Cobordism of Morse functions on surfaces, the universal complex of singular fibers and their application to map germs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Cobordism of Morse functions on surfaces, the universal complex of singular fibers and their application to map germs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-186988