On the homotopy type of the spaces of Morse functions on surfaces

Details On the homotopy type of the spaces of Morse functions on surfaces On the homotopy type of the spaces of Morse functions on surfaces

2011-04-25

arxiv.org/abs/1104.4796v3

Mathematics

Geometric Topology

32 pages, in Russian

Scientific paper

Let $M$ be a smooth closed orientable surface. Let $F$ be the space of Morse functions on $M$ having fixed number of critical points of each index, moreover at least $\chi(M)+1$ critical points are labeled by different labels (enumerated). A notion of a skew cylindric-polyhedral complex, which generalizes the notion of a polyhedral complex, is introduced. The skew cylindric-polyhedral complex $\mathbb{\widetilde K}$ (the "complex of framed Morse functions"), associated with the space $F$, is defined. In the case when $M=S^2$, the polyhedron $\mathbb{\widetilde K}$ is finite; its Euler characteristic is evaluated and the Morse inequalities for its Betti numbers are obtained. A relation between the homotopy types of the polyhedron $\mathbb{\widetilde K}$ and the space $F$ of Morse functions, endowed with the $C^\infty$-topology, is indicated.

Affiliated with

Also associated with

No associations

Rating

On the homotopy type of the spaces of Morse functions on 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 On the homotopy type of the spaces of Morse functions on surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the homotopy type of the spaces of Morse functions on surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-294884