Involutions on sapphire Sol 3-manifolds and the Borsuk-Ulam theorem for\n maps into Rⁿ

2014/10/01 by Alexandre Paiva Barreto, Barreto, Alexandre Paiva, Daciberg Lima Gonçalves +3
Mathematics · #55M20 #55M35 #57N10 #57S25 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1410.0142

openalex publication_date 2014/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For each sapphire Sol 3-manifold, we classify the free involutions. For\neach triple (M, \τ; Rⁿ) where M is a sapphire Sol 3-manifold and\n\τ is a free involution, we show if (M, \τ; Rⁿ) has the Borsuk-Ulam\nproperty or not. It is known that for n>3 the Borsuk-Ulam property does not\nhold independent of the involution, so we provide a classification when n=2\nand 3.\n

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