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A remark on Getzler's semi-classical approximation
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2012 (English)In: Geometry And Arithmetic, EMS Publishing House , 2012, 309-316 p.Conference paper, Published paper (Refereed)
Abstract [en]

Ezra Getzler notes in the proof of the main theorem of [Get98] that ”A proof of the theorem could no doubt be given using [a combinatorial interpretation in terms of a sum over necklaces]; however, we prefer to derive it directly from Theorem 2.2”. In this note we give such a direct combinatorial proof using wreath product symmetric functions.

Place, publisher, year, edition, pages
EMS Publishing House , 2012. 309-316 p.
Series
EMS Series of Congress Reports
Keyword [en]
Modular operads, graphical enumeration, tensor species
National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:kth:diva-48904DOI: 10.4171/119ISI: 000317792500018ISBN: 978-3-03719-119-4 (print)OAI: oai:DiVA.org:kth-48904DiVA: diva2:458840
Conference
Conference on Geometry and Arithmetic Location: Schiermonnikoog Isl, Netherlands Date: SEP 20-24, 2010
Note

QC 20130527

Available from: 2011-11-24 Created: 2011-11-24 Last updated: 2013-05-27Bibliographically approved
In thesis
1. Admissible covers, modular operads and modular forms
Open this publication in new window or tab >>Admissible covers, modular operads and modular forms
2011 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis contains three articles related to operads and moduli spaces of admissible covers of curves. In Paper A we isolate cohomology classes coming from modular forms inside a certain space of admissible covers, thereby showing that this moduli space can be used as a substitute for a Kuga–Sato variety. Paper B contains a combinatorial proof of Ezra Getzler’s semiclassical approximation for modular operads, and a proof of a formula needed in Paper A. In Paper C we explain in what sense spaces of admissible covers form a modular operad, by introducing the notion of an operad colored by a groupoid.

Abstract [sv]

Denna avhandling innehåller tre artiklar relaterade till operader och modulirum för godtagbara övertäckningar av kurvor. I artikel A isoleras kohomologiklasser associerade till modulära former inuti ett visst rum av godtag- bara övertäckningar, vilket visar att detta modulirum kan användas som ett substitut för en Kuga–Sato-varietet. Artikel B innehåller ett kombinatoriskt bevis av Ezra Getzlers semiklassiska approximation för modulära operader, och beviset av en formel som behövs i artikel A. I artikel C förklaras i vilken mening rum av tillåtbara övertäckningar utgör en modulär operad, nämligen en operad färgad av en gruppoid.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. vii, 20 p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 2011:09
National Category
Algebra and Logic
Identifiers
urn:nbn:se:kth:diva-48923 (URN)978-91-7501-179-0 (ISBN)
Presentation
2011-12-01, 3721, KTH, Lindstedtsvägen 25, Stockholm, 14:00 (English)
Opponent
Supervisors
Note
QC 20111124Available from: 2011-11-24 Created: 2011-11-24 Last updated: 2011-12-02Bibliographically approved

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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
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  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
More languages
Output format
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