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A Cohomological Obstruction to the Existence of ϕ-Equivariant Maps

2026/07/25 by Thales Fernando Vilamaior Paiva
Mathematics · #math.AT

paper · pdf

Abstract

Let ϕ: G→ H be a continuous homomorphism between compact Lie groups, let X be a G-space, and let Y be an H-space. We formulate a filtered change-of-groups obstruction to the existence of a ϕ-equivariant map X→ Y. We apply them to the inclusion of a finite cyclic group into the circle and to homomorphisms between tori acting coordinatewise on products of odd-dimensional spheres.

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