A Borsuk-Ulam Theorem for compact Lie group actions

Biasi, Carlos; Mattos, Denise de

doi:10.1007/s00574-006-0007-0

Cited by 9 publications

(6 citation statements)

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“…Theorem 3 generalizes, in a certain sense, the result of Cohen-Connet [4]. Generalizations of the same nature of the Borsuk-Ulam theorem with "nice" topological spaces X and Y satisfying some homological conditions can be found in [8] and [3].…”

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confidence: 57%

A note on the theorems of Lusternik–Schnirelmann and Borsuk–Ulam

Barros

Biasi

2008

Colloq. Math.

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Let p be a prime number and X a simply connected Hausdorff space equipped with a free Z p -action generated by f p : X → X. Let α : S 2n−1 → S 2n−1 be a homeomorphism generating a free Z p -action on the (2n − 1)-sphere, whose orbit space is some lens space. We prove that, under some homotopy conditions on X, there exists an equivariant map F : (S 2n−1 , α) → (X, f p ). As applications, we derive new versions of generalized Lusternik-Schnirelmann and Borsuk-Ulam theorems.2000 Mathematics Subject Classification: Primary 55M20; Secondary 55M30, 55M35.

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confidence: 57%

A note on the theorems of Lusternik–Schnirelmann and Borsuk–Ulam

Barros

Biasi

2008

Colloq. Math.

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“…An alternative, but relatively simple, proof of the later theorem was also given by Dold [2] in 1983. There are also some other generalizations of the result, see for example [1]. In this note, we give a simple proof of the above result for free actions of the cyclic group Z p of prime order p involving only elementary algebraic topology.…”

Section: Introductionmentioning

confidence: 65%

A simple proof of the Borsuk-Ulam theorem for Z_p-actions

Singh¹

2010

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“…Going beyond Z 2 . Among generalizations to other groups G, whose noncommutative analogues in our opinion might be most accessible, are certain necessary homological conditions for the existence of a G-equivariant map f : S(W ) → S(V ) of spheres in the vector spaces W, V of orthogonal representations of a compact Lie group G [13] and of Hausdorff, pathwise connected and paracompact free G-spaces [3].…”

Section: 2mentioning

confidence: 99%