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Homologies of Moduli Space M 2,1

Abstract

We consider the open moduli space M 2,1 of complex curves of genus 2 with one marked point. Using the language of chord diagrams, we describe the cell structure of M 2,1 and cell adjacency. This allows us to construct matrices of boundary operators and compute Betty numbers of M 2,1 over ℚ.

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Correspondence to Yu. Yu. Kochetkov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 19, No. 1, pp. 45–63, 2014.

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Kochetkov, Y.Y. Homologies of Moduli Space M 2,1 . J Math Sci 211, 327–340 (2015). https://doi.org/10.1007/s10958-015-2609-9

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Keywords

  • Modulus Space
  • Boundary Operator
  • Cyclic Group
  • Marked Point
  • Euler Characteristic