Fatgraph Algorithms and the Homology of the Kontsevich Complex

Details Fatgraph Algorithms and the Homology of the Kontsevich Complex Fatgraph Algorithms and the Homology of the Kontsevich Complex

2012-02-08

arxiv.org/abs/1202.1820v2

Mathematics

Algebraic Geometry

61 pages, 12 figures. Corrected attributions, claims, and bibliography

Scientific paper

Fatgraphs are multigraphs enriched with a cyclic order of the edges incident to a vertex. This paper presents algorithms to: (1) generate the set of all fatgraphs having a given genus and number of boundary cycles; (2) compute automorphisms of any given fatgraph; (3) compute the homology of the fatgraph complex. The algorithms are suitable for effective computer implementation. In particular, this allows us to compute the rational homology of the moduli space of Riemann surfaces with marked points. We thus compute the Betti numbers of $M_{g,n}$ with $(2g + n) \leq 6$, corroborating known results.

Affiliated with

Also associated with

No associations

Rating

Fatgraph Algorithms and the Homology of the Kontsevich Complex 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 Fatgraph Algorithms and the Homology of the Kontsevich Complex, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fatgraph Algorithms and the Homology of the Kontsevich Complex will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-156034