The Borsuk-Ulam theorem for 3-manifolds
The Borsuk-Ulam theorem for 3-manifolds
We study the Borsuk-Ulam theorem for triple (M, τ, ℝn), where M is a compact, connected, 3-manifold equipped with a fixed-point-free involution τ. The largest value of n for which the Borsuk-Ulam theorem holds is called the ℤ2-index and in our case it takes value 1, 2 or 3. We …