scholarly journals On closed subgroups of the group of homeomorphisms of a manifold

10.5802/jep.7 ◽  
2014 ◽  
Vol 1 ◽  
pp. 147-159
Author(s):  
Frédéric Le Roux
Keyword(s):  
Group Of Homeomorphisms

scholarly journals Normal subgroups of diffeomorphism and homeomorphism groups of ℝn and other open manifolds

2011 ◽  
Vol 31 (6) ◽  
pp. 1835-1847 ◽  
Author(s):  
PAUL A. SCHWEITZER, S. J.
Keyword(s):  
Normal Subgroup ◽  
Compact Manifold ◽  
Normal Subgroups ◽  
Open Manifold ◽  
Open Manifolds ◽  
Group Of Homeomorphisms ◽  
Homeomorphism Groups

AbstractWe determine all the normal subgroups of the group of Cr diffeomorphisms of ℝn, 1≤r≤∞, except when r=n+1 or n=4, and also of the group of homeomorphisms of ℝn ( r=0). We also study the group A0 of diffeomorphisms of an open manifold M that are isotopic to the identity. If M is the interior of a compact manifold with non-empty boundary, then the quotient of A0 by the normal subgroup of diffeomorphisms that coincide with the identity near to a given end e of M is simple.

Probabilistic convergence transformation groups

2018 ◽  
Vol 68 (6) ◽  
pp. 1447-1464 ◽  
Author(s):  
T. M. G. Ahsanullah ◽  
Gunther Jäger
Keyword(s):  
Transformation Group ◽  
Convergence Space ◽  
Probabilistic Metric Space ◽  
Arbitrary Group ◽  
Convergence Group ◽  
Group Of Homeomorphisms ◽  
Convergence Structure ◽  
Probabilistic Metric ◽  
Probabilistic Convergence Space ◽  
Natural Way

Abstract We introduce a notion of a probabilistic convergence transformation group, and present various natural examples including quotient probabilistic convergence transformation group. In doing so, we construct a probabilistic convergence structure on the group of homeomorphisms and look into a probabilistic convergence group that arises from probabilistic uniform convergence structure on function spaces. Given a probabilistic convergence space, and an arbitrary group, we construct a probabilistic convergence transformation group. Introducing a notion of a probabilistic metric convergence transformation group on a probabilistic metric space, we obtain in a natural way a probabilistic convergence transformation group.

Acyclicity of Certain Homeomorphism Groups

1990 ◽  
Vol 42 (1) ◽  
pp. 80-94 ◽  
Author(s):  
P. Sankaran ◽  
K. Varadarajan
Keyword(s):  
Compact Support ◽  
Natural Question ◽  
Bounded Support ◽  
Group Of Homeomorphisms ◽  
Group A ◽  
Homeomorphism Groups

The concept of a mitotic group was introduced in [3] by Baumslag, Dyer and Heller who showed that mitotic groups were acyclic. In [8] one of the authors introduced the concept of a pseudo-mitotic group, a concept weaker than that of a mitotic group, and showed that pseudo-mitotic groups were acyclic and that the group Gnof homeomorphisms of Rn with compact support is pseudo-mitotic. In our present paper we develop techniques to prove pseudomitoticity of certain other homeomorphism groups. In [5] Kan and Thurston observed that the group of set theoretic bijections of Q with bounded support is acyclic. A natural question is to decide whether the group of homeomorphisms of Q (resp. the irrationals I ) with bounded support is acyclic or not. In the present paper we develop techniques to answer this question in the affirmative.

scholarly journals On projective lift and orbit spaces

1994 ◽  
Vol 50 (3) ◽  
pp. 445-449 ◽  
Author(s):  
T.K. Das
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Covariant Functor ◽  
Hausdorff Spaces ◽  
Orbit Spaces ◽  
Locally Compact ◽  
Discontinuous Group ◽  
Coreflective Subcategory ◽  
Group Of Homeomorphisms ◽  
Locally Compact Hausdorff Space

By constructing the projective lift of a dp-epimorphism, we find a covariant functor E from the category Cd of regular Hausdorff spaces and continuous dp-epimorphisms to its coreflective subcategory εd consisting of projective objects of Cd We use E to show that E(X/G) is homeomorphic to EX/G whenever G is a properly discontinuous group of homeomorphisms of a locally compact Hausdorff space X and X/G is an object of Cd.

scholarly journals Minimal Spaces with Cyclic Group of Homeomorphisms

2015 ◽  
Vol 29 (1) ◽  
pp. 243-257 ◽  
Author(s):  
Tomasz Downarowicz ◽  
L’ubomír Snoha ◽  
Dariusz Tywoniuk
Keyword(s):  
Cyclic Group ◽  
Group Of Homeomorphisms

t-Representability of maximal subgroups of symmetric groups

2018 ◽  
Vol 9 (1) ◽  
pp. 27
Author(s):  
Sini P
Keyword(s):  
Symmetric Group ◽  
Symmetric Groups ◽  
Maximal Subgroups ◽  
Group Of Homeomorphisms

A subgroup \(H\) of the group \(S(X)\) of all permutations of a set \(X\) is called \(t\)−representable on \(X\) if there exists a topology \(T\) on \(X\) such that the group of homeomorphisms of \((X, T ) = K\). In this paper we study the \(t\)-representability of maximal subgroups of the symmetric group.

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