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The moduli space of real curves and a Z/2-equivariant Madsen-Weiss theorem

Author: Nisan Alexander Stiennon; Søren Galatius; Thomas Church; Ralph L Cohen; Stanford University. Department of Mathematics.
Publisher: 2013.
Dissertation: Thesis (Ph.D.)--Stanford University, 2013.
Edition/Format:   Thesis/dissertation : Document : Thesis/dissertation : eBook   Computer File : English
Database:WorldCat
Summary:
Galatius, Madsen, Tillmann, and Weiss proved that the classifying space of the category of 2-cobordisms is equivalent to the loopspace of a particular Thom spectrum. We show that this is in fact a Z/2-equivariant equivalence, where we equip all spaces with a Z/2-action which is motivated by complex conjugation of complex curves. In order to do this, we prove an equivariant delooping theorem which shows that  Read more...
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Details

Material Type: Document, Thesis/dissertation, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Nisan Alexander Stiennon; Søren Galatius; Thomas Church; Ralph L Cohen; Stanford University. Department of Mathematics.
OCLC Number: 849237450
Notes: Submitted to the Department of Mathematics.
Description: 1 online resource.
Responsibility: Nisan Alexander Stiennon.

Abstract:

Galatius, Madsen, Tillmann, and Weiss proved that the classifying space of the category of 2-cobordisms is equivalent to the loopspace of a particular Thom spectrum. We show that this is in fact a Z/2-equivariant equivalence, where we equip all spaces with a Z/2-action which is motivated by complex conjugation of complex curves. In order to do this, we prove an equivariant delooping theorem which shows that grouplike topological monoids with Z/2-action are Z/2-equivalent to loopspaces. Furthermore, we motivate our choice of Z/2-action by showing that it determines a Z/2-space BDiff_g whose fixed points classify real curves.

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