Calculating the Euler Characteristic of the Moduli Space of Curves View Full Text


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Article Info

DATE

2022-02-18

AUTHORS

Bodo Lass

ABSTRACT

The orbifold Euler characteristic of the moduli space ℳg;1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\cal M}_{g;1}}$$\end{document} of genus g smooth curves with one marked point (g ≥ 1) was calculated by Harer and Zagier: χ(ℳg;1)=ζ(1−2g)=−B2g/(2g)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\chi ({{\cal M}_{g;1}}) = \zeta (1 - 2g) = - {B_{2g}}/(2g)$$\end{document}, where ζ is the Riemann zeta function and B2g is the (2g)th Bernoulli number. We give a shorter proof of this result using only formal power series and classical combinatorics. More... »

PAGES

1-14

References to SciGraph publications

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URI

http://scigraph.springernature.com/pub.10.1007/s00493-021-4688-1

DOI

http://dx.doi.org/10.1007/s00493-021-4688-1

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https://app.dimensions.ai/details/publication/pub.1145698748


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