All Questions

I meet this problem when reading Rolfsen's Knots&Links. After giving 8 different definitions of linking number for knots in $S^3$, he left an exercise: Given disjoint PL knots $J$ and $K$ in $S^3=\...

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 ...

Consider the space $K$ of all immersions of $S^1$ into $\mathbb R^3$. The set of knots with self-intersection is a discriminant in $K$ and divide it into "chambers". Let $f$ be a knot with $n$ double ...

Suppose that $K$ is an $\textit{alternating}$ knot in $S^3$, and let $R_0$ be the space of homomorphisms from $\pi_1(S^3 - K)\to SU(2)$ which send meridians to trace free matrices. Denote the subset ...