All Questions

In 3-manifold topology, the notion of Seifert surface is well known. It is then used to define link numbers of knots. Question: Consider embedding $N^n \rightarrow M^{2n+1}$ of n-dimensional manifold $...

This question regards a part of the proof of the so called surgery step, in Wall's book "surgery on compact manifolds", Theorem 1.1. Setting $M^m$ smooth manifold, $X$ CW complex, $\phi :M\...

I'm studying the article "An alternative proof of Lickorish–Wallace theorem" (doi link) and I got stuck in a problem. Let $H_g$ be a 3 dimensional handlebody of genus $g$, a primate curve in ...

In Barden's 1965 paper: Simply-connected five manifolds, Barden gave a complete list of diffeomorphism classes of simply-connected 5-manifolds: $$X_{j,k_1,\dots,k_n}=X_j\#M_{k_1}\#\cdots\#M_{k_n}$$ ...

We like to ask for the comparison of two topologies of three 2-tori inside the same 4-manifolds glued from two different diffeomorphisms (see the end). Given an embedded torus $T$ with trivial normal ...

What are some of the most symmetric configurations of four 2-surfaces linked in the 4-dimensional sphere $S^4$? To make a lower-dimensional analogy, recall that in 3-dimensional sphere $S^3$, we can ...