Associativity: Loop spaces and topological groups

Stochastic processes on totally disconnected topological groups are investigated. In particular, they are considered for diffeomorphism groups and loop groups of manifolds on non-Archimedean Banach spaces. Theorems about a quasi-invariance and a pseudodifferentiability of transition measures are proved. Transition measures are used for the construction of strongly continuous representations including the irreducible ones of these groups. In addition, stochastic processes on general Banach-Lie groups, loop monoids, loop spaces, and path spaces of manifolds on Banach spaces over non-Archimedean local fields are also investigated.

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SOME PROPERTIES OF G-SPACES ACTED WITH TOPOLOGICAL GROUPS

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.7.56 ◽

2020 ◽

Vol 9 (7) ◽

pp. 4917-4922

Author(s):

S. Sivakumar ◽

D. Lohanayaki

Keyword(s):

Topological Groups

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Homomorphisms of topological groups that cannot be factorized by weight and dimension

Mathematical Notes ◽

10.1007/bf01158253 ◽

1987 ◽

Vol 41 (3) ◽

pp. 226-228

Author(s):

V. G. Pestov

Keyword(s):

Topological Groups

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CONTINUITY OF MEASURABLE HOMOMORPHISMS

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972708000610 ◽

2008 ◽

Vol 78 (1) ◽

pp. 171-176 ◽

Cited By ~ 2

Author(s):

JANUSZ BRZDȨK

Keyword(s):

Topological Group ◽

Abelian Group ◽

Baire Property ◽

Topological Groups ◽

Locally Compact ◽

Compact Topological Group ◽

Locally Compact Topological Group

AbstractWe give some general results concerning continuity of measurable homomorphisms of topological groups. As a consequence we show that a Christensen measurable homomorphism of a Polish abelian group into a locally compact topological group is continuous. We also obtain similar results for the universally measurable homomorphisms and the homomorphisms that have the Baire property.

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On the Dimension Modulo Classes of Topological Spaces and Free Topological Groups

Georgian Mathematical Journal ◽

10.1515/gmj.2003.209 ◽

2003 ◽

Vol 10 (2) ◽

pp. 209-222

Author(s):

I. Bakhia

Keyword(s):

Wide Class ◽

Sufficient Conditions ◽

Topological Spaces ◽

Topological Groups ◽

Compact Spaces ◽

Topological Semigroups

Abstract Functions of dimension modulo a (rather wide) class of spaces are considered and the conditions are found, under which the dimension of the product of spaces modulo these classes is equal to zero. Based on these results, the sufficient conditions are established, under which spaces of free topological semigroups (in the sense of Marxen) and spaces of free topological groups (in the sense of Markov and Graev) are zero-dimensional modulo classes of compact spaces.

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Homological epimorphisms, homotopy epimorphisms and acyclic maps

Forum Mathematicum ◽

10.1515/forum-2019-0249 ◽

2020 ◽

Vol 32 (6) ◽

pp. 1395-1406

Author(s):

Joseph Chuang ◽

Andrey Lazarev

Keyword(s):

Wide Class ◽

Topological Spaces ◽

Loop Spaces ◽

Graded Algebras ◽

Differential Graded Algebras ◽

Algebraic Description ◽

Acyclic Map ◽

Induced Maps

AbstractWe show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of induced maps of their chain algebras of based loop spaces. In the case of a universal acyclic map we obtain, for a wide class of spaces, an explicit algebraic description for these induced maps in terms of derived localization.

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