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arXiv:1202.1820math.AG

Fatgraph Algorithms and the Homology of the Kontsevich Complex

Riccardo Murri

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Abstract

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.

arXiv comments
61 pages, 12 figures. Corrected attributions, claims, and bibliography
Journal reference
DOI
Subjects
math.AGAlgebraic Geometry cs.CGComputational Geometry cs.MSMathematical Software math.GTGeometric Topology

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  1. Performance of Python runtimes on a non-numeric scientific code 1 comment

    • It's a conference paper, from EuroSciPy 2013, distributed through a preprint service. There's no expectation it will be a high quality paper. Instead, it's an appropriate quality for where and how it was published. "What algorithms were used"? The papers says "The code used to…

      dalkeView on HNParent context

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