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

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          Abstract

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

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          The F2 Cohomology of Sol^3-Manifolds

          We compute the rings H(N;F2) for N a closed Sol3-manifold and then determine the Borsuk-Ulam indices BU(N,ϕ) with ϕ0 in H1(N;F2).
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            The Borsuk-Ulam theorem for homotopy spherical space forms

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              Author and article information

              Journal
              2014-10-01
              2014-11-13
              Article
              1410.0142
              d18a82be-7fa1-47e1-814d-cf220a4510ad

              http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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              Custom metadata
              55M20, 57N10, 55M35, 57S25
              17 pages
              math.AT

              Geometry & Topology
              Geometry & Topology

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