Moduli spaces of Riemann surfaces as Hurwitz spaces
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We consider the moduli space Mg,n of Riemann surfaces of genus g≥0 with n≥1 ordered and directed marked points. For d≥2g+n−1 we show that Mg,n is homotopy equivalent to a component of the simplicial Hurwitz space HurΔ(Sdgeo) associated with the partially multiplicative quandle Sdgeo. As an application, we give a new proof of the Mumford conjecture on the stable rational cohomology of moduli spaces of Riemann surfaces. We also provide a combinatorial model for the infinite loop space Ω∞−2MTSO(2) of Hurwitz flavour.
Original language | English |
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Article number | 109217 |
Journal | Advances in Mathematics |
Volume | 430 |
Number of pages | 52 |
ISSN | 0001-8708 |
DOIs | |
Publication status | Published - 2023 |
Bibliographical note
Publisher Copyright:
© 2023 Elsevier Inc.
- Group completion, Hurwitz space, Moduli space, Riemann-Roch
Research areas
ID: 369246681