Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locally homogeneous geometric manifolds   Motivated by Felix Klein's notion that geometry is governed by its group of
symmetry transformations, Charles Ehresmann initiated the study of geometric
structures on topological spaces locally modeled on a homogeneous space of a
Lie group. These locally homogeneous spaces later formed the context of
Thurston's 3-dimensional geometrization program. The basic problem is for a
given topology S and a geometry X = G/H, to classify all the possible ways of
introducing the local geometry of G/H into S. For example, a sphere admits no
local Euclidean geometry: there is no metrically accurate Euclidean atlas of
the earth. One develops a space whose points are equivalence classes of
geometric structures on S, which itself exhibits a rich geometry and symmetries
arising from the topological symmetries of S. In this talk I will survey
several examples of the classification of locally homogeneous geometric
structures on manifolds in low dimension, and how it leads to a general study
of surface group representations. In particular geometric structures are a
useful tool in understanding local and global properties of deformation spaces
of representations of fundamental groups.

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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph