Questions tagged [finite-type-invariants]

Let $\mathcal K_n$ be the set of all $n$-singular knots up to isotopy,i.e. an immersion of $S^1$ into $\mathbb R^3$ with $n$ transverse double points that is an embedding when restricted to the ...

For an (oriented) knot in $S^3$ the number $\Gamma(K) := \Delta_K’’(1)$ shows up in a number of places in knot theory, for example the Casson-Walker-Lescop invariant. Here $\Delta_K(t)$ is the ...

Let $\mathcal{K}$ be the commutative monoid whose elements are (isotopy) equivalence classes of knots with composition under the connected knot sum, and $\mathbb{Z}\mathcal{K}$ be the corresponding ...

The abelian group of $k$-chord diagrams on a skeleton of two directed line segments (modulo the STU relation), $\mathcal A_k(\uparrow\uparrow)$, is known to have $2$-torsion when $k=5$. In fact, I ...

Recall that there are knots in $\mathbf{R}^3$ that are not invertible, i.e. not isotopic to themselves with the orientation reversed. However, it is not easy to tell whether or not a given knot is ...