Displaying similar documents to “Topological classification of multiaxial U ( n ) -actions (with an appendix by Jared Bass)”

Involutions on tori with codimension-one fixed point set

Allan L. Edmonds (2009)

Colloquium Mathematicae

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The standard P. A. Smith theory of p-group actions on spheres, disks, and euclidean spaces is extended to the case of p-group actions on tori (i.e., products of circles) and coupled with topological surgery theory to give a complete topological classification, valid in all dimensions, of the locally linear, orientation-reversing, involutions on tori with fixed point set of codimension one.

ℂ * -actions on ℂ 3 are linearizable.

Kaliman, Shulim I., Koras, Mariusz, Makar-Limanov, Leonid, Russell, Peter (1997)

Electronic Research Announcements of the American Mathematical Society [electronic only]

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A study of remainders of topological groups

A. V. Arhangel'skii (2009)

Fundamenta Mathematicae

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Some duality theorems relating properties of topological groups to properties of their remainders are established. It is shown that no Dowker space can be a remainder of a topological group. Perfect normality of a remainder of a topological group is consistently equivalent to hereditary Lindelöfness of this remainder. No L-space can be a remainder of a non-locally compact topological group. Normality is equivalent to collectionwise normality for remainders of topological groups. If a...

A ratio ergodic theorem for multiparameter non-singular actions

Michael Hochman (2010)

Journal of the European Mathematical Society

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We prove a ratio ergodic theorem for non-singular free ℤ d and ℝ d actions, along balls in an arbitrary norm. Using a Chacon–Ornstein type lemma the proof is reduced to a statement about the amount of mass of a probability measure that can concentrate on (thickened) boundaries of balls in ℝ d . The proof relies on geometric properties of norms, including the Besicovitch covering lemma and the fact that boundaries of balls have lower dimension than the ambient space. We also show that for general...

Arhangel'skiĭ sheaf amalgamations in topological groups

Boaz Tsaban, Lyubomyr Zdomskyy (2016)

Fundamenta Mathematicae

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We consider amalgamation properties of convergent sequences in topological groups and topological vector spaces. The main result of this paper is that, for arbitrary topological groups, Nyikos’s property α 1 . 5 is equivalent to Arhangel’skiĭ’s formally stronger property α₁. This result solves a problem of Shakhmatov (2002), and its proof uses a new perturbation argument. We also prove that there is a topological space X such that the space C p ( X ) of continuous real-valued functions on X with the...

Foliations by planes and Lie group actions

J. A. Álvarez López, J. L. Arraut, C. Biasi (2003)

Annales Polonici Mathematici

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Let N be a closed orientable n-manifold, n ≥ 3, and K a compact non-empty subset. We prove that the existence of a transversally orientable codimension one foliation on N∖K with leaves homeomorphic to ℝ n - 1 , in the relative topology, implies that K must be connected. If in addition one imposes some restrictions on the homology of K, then N must be a homotopy sphere. Next we consider C² actions of a Lie group diffeomorphic to ℝ n - 1 on N and obtain our main result: if K, the set of singular points...

Continuous actions of pseudocompact groups and axioms of topological group

Alexander V. Korovin (1992)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we show that it is possible to extend the Ellis theorem, establishing the relations between axioms of a topological group on a new class 𝒩 of spaces containing all countably compact spaces in the case of Abelian group structure. We extend statements of the Ellis theorem concerning separate and joint continuity of group inverse on the class of spaces 𝒩 that gives some new examples and statements for the C p -theory and theory of topologically homogeneous spaces.