Borsuk-Ulam theorems for elementary abelian 2-groups

DOI10.12775/tmna.2022.042zbMath1516.55001arXiv2201.09564WikidataQ121667664 ScholiaQ121667664MaRDI QIDQ6044503

Michael Crabb

Publication date: 19 May 2023

Published in: Topological Methods in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.09564

zbMATH Keywords

Euler classBorsuk-Ulam theoremequivariant mappingBourgin-Yang theorem

Mathematics Subject Classification ID

Sphere bundles and vector bundles in algebraic topology (55R25) Degree, winding number (55M25) Finite groups of transformations in algebraic topology (including Smith theory) (55M35) Equivariant homology and cohomology in algebraic topology (55N91) Fixed points and coincidences in algebraic topology (55M20)

Cites Work

• Aspects of the Borsuk-Ulam theorem
• Some remarks on the parametrized Borsuk-Ulam theorem
• Borsuk-Ulam type theorems on product spaces. II
• Borsuk-Ulam theorem for the loop space of a sphere
• Polynomial partitioning for several sets of varieties
• General Bourgin-Yang theorems
• Bourgin-Yang version of the Borsuk-Ulam theorem for \(\mathbb Z_{p^{k}}\)-equivariant maps
• Extensions of theorems of Rattray and Makeev
• Borsuk-Ulam theorems for products of spheres and Stiefel manifolds revisited
• Connective \(K\)-theory and the Borsuk-Ulam theorem
• Bourgin-Yang versions of the Borsuk-Ulam theorem for \(p\)-toral groups
• On the Borsuk-Ulam theorem for \(Z_{p^ a}\) actions on \(S^{2n-1}\) and maps \(S^{2n-1} \to R^ m\)
• An ideal-valued cohomological index theory with applications to Borsuk—Ulam and Bourgin—Yang theorems
• A Continuous Version of the Borsuk-Ulam Theorem
• Borsuk-Ulam Theorems for Arbitrary S 1 Actions and Applications
• Polynomial partitioning for a set of varieties
• Equivariant maps between representation spheres

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