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  Pillowcase covers: counting Feynman-like graphs associated with quadratic differentials

Goujard, E., & Möller, M. (2020). Pillowcase covers: counting Feynman-like graphs associated with quadratic differentials. Algebraic & Geometric Topology, 20(5), 2451-2510. doi:10.2140/agt.2020.20.2451.

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Goujard-Möller_Pillowcase covers_2020.pdf (Publisher version), 679KB
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Goujard-Möller_Pillowcase covers_2020.pdf
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Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer Allianz- bzw. Nationallizenz frei zugänglich. / This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence respectively.
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https://doi.org/10.2140/agt.2020.20.2451 (Publisher version)
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 Creators:
Goujard, Elise1, Author           
Möller, Martin1, Author           
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Geometric Topology, Algebraic Geometry, Number Theory
 Abstract: We prove the quasimodularity of generating functions for counting pillowcase
covers, with and without Siegel-Veech weight. Similar to prior work on torus
covers, the proof is based on analyzing decompositions of half-translation
surfaces into horizontal cylinders. It provides an alternative proof of the
quasimodularity results of Eskin-Okounkov and a practical method to compute
area Siegel-Veech constants. A main new technical tool is a quasi-polynomiality
result for 2-orbifold Hurwitz numbers with completed cycles.

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Language(s): eng - English
 Dates: 2020
 Publication Status: Issued
 Pages: 60
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 1809.05016
DOI: 10.2140/agt.2020.20.2451
 Degree: -

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Title: Algebraic & Geometric Topology
  Abbreviation : Algebr. Geom. Topol.
Source Genre: Journal
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Publ. Info: Mathematical Sciences Publishers
Pages: - Volume / Issue: 20 (5) Sequence Number: - Start / End Page: 2451 - 2510 Identifier: -