All Questions

Does every triangulable manifold have a vertex-transitive triangulation? When I talk about a vertex-transitive triangulation of a manifold, I mean in the sense of realizing a manifold homeomorphically ...

Piece-wise linear manifolds are combinatorially represented by simplicial complexes modulo Pachner moves. However, for dimensions greater than $3$, the notions of piece-wise linear and topological ...

I am interested in the barycentric subdivision of closed homology manifolds. Definition A (finite) simplicial complex $K$ is a closed homology manifold of dimension $n$ if for every $k$-simplex, its ...

We know that there are non-triangulable 4-manifolds, such as the E$_8$ manifold. Can E$_8$ manifold be a boundary of some 5-manifold $M_5$? Can such a $M_5$ be triangulable or non-triangulable? What ...

We know "Any closed, oriented $3$-manifold $M$ is the boundary of some oriented $4$-manifold $B$." See this post: Elegant proof that any closed, oriented 3-manifold is the boundary of some ...

This question is only motivated by curiosity; I don't know a lot about manifold topology. Suppose $M$ is a compact topological manifold of dimension $n$. I'll assume $n$ is large, say $n\geq 4$. The ...