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On the operad structure of admissible G-covers
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We describe the modular operad structure on the moduli spaces of pointed stable curves equipped with an admissible G-cover. To do this we are forced to introduce the notion of an operad colored not by a set but by the objects of a groupoid. This construction interpolates in some sense between “framed” and “colored” versions of operads; we hope that it will be of independent interest. An algebra over this operad is the same thing as a G-equivariant CohFT. Our main theorem is an extension of the symmetric function formalism for modular operads to this setting; we prove an analogue of the formula of Getzler and Kapranov describing the effect of the “free modular operad” functor on the level of symmetric functions.

National Category
Algebra and Logic
Identifiers
URN: urn:nbn:se:kth:diva-48902OAI: oai:DiVA.org:kth-48902DiVA: diva2:458839
Note

QS 2011

Available from: 2011-11-24 Created: 2011-11-24 Last updated: 2013-05-20Bibliographically 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
2. Topology of moduli spaces and operads
Open this publication in new window or tab >>Topology of moduli spaces and operads
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2013. vii, 45 p.
Series
Trita-MAT. MA, ISSN 1401-2278 ; 13:02
National Category
Geometry
Identifiers
urn:nbn:se:kth:diva-122389 (URN)978-91-7501-759-4 (ISBN)
Public defence
2013-05-31, Sal E2, Lindstedtsvägen 3, KTH, Stockholm, 14:00 (English)
Opponent
Supervisors
Note

QC 20130520

Available from: 2013-05-20 Created: 2013-05-20 Last updated: 2013-05-20Bibliographically approved

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Citation style
  • apa
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