7,227 research outputs found
When is the underlying space of an orbifold a manifold?
We classify orthogonal actions of finite groups on Euclidean vector spaces
for which the corresponding quotient space is a topological, homological or
Lipschitz manifold, possibly with boundary. In particular, our results answer
the question of when the underlying space of an orbifold is a manifold.Comment: 29 pages, combined with former arXiv:1509.06796, title updated, to
appear in Trans. Amer. Math. So
Equivariant smoothing of piecewise linear manifolds
We prove that every piecewise linear manifold of dimension up to four on
which a finite group acts by piecewise linear homeomorphisms admits a
compatible smooth structure with respect to which the group acts smoothly. This
solves a challenge posed by Thurston in dimension three and confirms a
conjecture by Kwasik and Lee in dimension four in a stronger form.Comment: revised version, accepted by Math. Proc. Cambridge Philos. So
Characterization of finite groups generated by reflections and rotations
We characterize finite groups G generated by orthogonal transformations in a
finite-dimensional Euclidean space V whose fixed point subspace has codimension
one or two in terms of the corresponding quotient space V/G with its quotient
piecewise linear structure.Comment: revised version, accepted by Journal of Topolog
Classification of finite groups generated by reflections and rotations
We survey the existing parts of a classification of finite groups generated
by orthogonal transformations in a finite-dimensional Euclidean space whose
fixed point subspace has codimension one or two and extend it to a complete
classification. These groups naturally arise in the study of the quotient of a
Euclidean space by a finite orthogonal group and hence in the theory of
orbifolds.Comment: 38 pages, accepted by Transformation Group
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