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Before starting my question I want to write something that I already know. Borel Conjecture: Any homotopy equivalence between two closed aspherical manifolds is homotopic to a homeomorphism. Now, my ...

I'm reading Kauffman's 1990 paper "An Invariant of Regular Isotopy" about knots that are isotopic through only Reidemeister Type II and III moves, which is known as a regular isotopy. His ...

Question: What is the first appearance in the literature of one of the following statements: The result of intersecting a simplex with a cell of the dual subdivision is a cube There is a coherent ...

Let $S^k$ be a topological $k$-dimensional sphere. Let $D^k$ be a $k$ dimensional disk that includes in $S^k$. Let $q: D^k \to D^r$ be a map and $r \leq k$. Let $$W = S^k \sqcup D^r/\sim$$ where $S^...

In an old answer to an old question of mine, Peter Teichner commented that it is an open problem to determine which homotopy 2-types arise from 4-manifolds. In some instances we know that a 4-manifold ...

Consider the set of homeomorphisms of the topological n-ball to itself with the compact open topology. Sitting inside this space of homeomorphisms are particular subspaces. The first subspace is those ...