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september 2019 Moduli Spaces of Affine Homogeneous Spaces
Gregor Weingart
Bull. Belg. Math. Soc. Simon Stevin 26(3): 365-400 (september 2019). DOI: 10.36045/bbms/1568685653

Abstract

Every affine homogeneous space is locally described by its curvature, its torsion and a slightly less tangible object, its connection. Using this description of the local geometry of an affine homogeneous space we construct a variety $\mathfrak{M}(\,\mathfrak{g}\,V\,)$, which serves as a coarse moduli space for the local isometry classes of affine homogeneous spaces. Infinitesimal deformations of an isometry class of affine homogeneous spaces in this moduli space are \linebreak described by the Spencer cohomology of a comodule associated to a point in $\mathfrak{M}_\infty(\,\mathfrak{g}\,V\,)$. In an appendix we discuss the relevance of this construction to the study of locally homogeneous spaces.

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Gregor Weingart. "Moduli Spaces of Affine Homogeneous Spaces." Bull. Belg. Math. Soc. Simon Stevin 26 (3) 365 - 400, september 2019. https://doi.org/10.36045/bbms/1568685653

Information

Published: september 2019
First available in Project Euclid: 17 September 2019

zbMATH: 07120721
MathSciNet: MR4007604
Digital Object Identifier: 10.36045/bbms/1568685653

Subjects:
Primary: 22F30, 53C30

Rights: Copyright © 2019 The Belgian Mathematical Society

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Vol.26 • No. 3 • september 2019
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