Path-components of Morse mappings spaces of surfaces

Details Path-components of Morse mappings spaces of surfaces Path-components of Morse mappings spaces of surfaces

1999-10-18

arxiv.org/abs/math/9910085v3

Comm. Math. Helv. 80 (2005), 655-690

Mathematics

Geometric Topology

LaTex2e, 33 pages, 26 figures (eps) Now the proof is given for all compact orientable and non-orientable surfaces

Scientific paper

Let M be a compact surface and P be one dimensional manifold without boundary, that is the line R^1 or a circle S^1. The classification of path-components of the space of Morse maps from M into P was recently obtained by S.V.Matveev and V.V.Sharko for the case P=R^1. For P=S^1 the classification was obtained by the author. All this results can be reformulated as one theorem: "Two Morse maps f,g:M \to P belong to the same path component of a space of Morse mappings from M into P if and only if they are homotopic and have the same number of crutucal points in each index and the same sets of positive and negative boundary circles". Here we give another independent proof of this theorem based on Lickorich's theorem on generators of homeotopy group of surface.

Affiliated with

Also associated with

No associations

Rating

Path-components of Morse mappings spaces of surfaces 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 Path-components of Morse mappings spaces of surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Path-components of Morse mappings spaces of surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-325416