Moduli spaces of affine homogeneous spaces

DOI10.36045/BBMS/1568685653zbMATH Open1436.53034arXiv1707.06385OpenAlexW2974705179MaRDI QIDQ2330475

Publication date: 22 October 2019

Published in: Bulletin of the Belgian Mathematical Society - Simon Stevin (Search for Journal in Brave)

Abstract: Apart from global topological problems an affine homogeneous space is locally described by its curvature, its torsion and a slightly less tangible object called its connection in a given base point. Using this description of the local geometry of an affine homogeneous space we construct an algebraic variety

m a t h f r a k M (m a t h f r a k g l, V)

, which serves as a coarse moduli space for the local isometry classes of affine homogeneous spaces of dimension dim V. Moreover we associate a

m a t h r m S y m V^{*}

-comodule to a point in

m a t h f r a k M (m a t h f r a k g l, V,)

and use its Spencer cohomology in order to describes the infinitesimal deformations of this point in the true moduli space

m a t h f r a k M_{i} n f t y (m a t h f r a k g l, V,)

.

Full work available at URL: https://arxiv.org/abs/1707.06385

zbMATH Keywords

torsion curvature deformation theory connection isometry class locally homogeneous space

Mathematics Subject Classification ID

Homogeneous spaces (22F30) Differential geometry of homogeneous manifolds (53C30) Discrete subgroups of Lie groups (22E40) Group actions on manifolds and cell complexes in low dimensions (57M60) Topological transformation groups (57Sxx)

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