We extend the theory of Vassiliev (or finite type) invariants for knots to knotoids using two different approaches. Firstly, we take closures on obtain and use knots, proving that these are knotoid isotopy invariant. Secondly, define type directly knotoids, by extending singular via skein relation. Then, spherical show there non-trivial type-1 invariants, in contrast with classical knot where v...

In 1987 Squier defined the notion of finite derivation type for a finitely presented monoid. To do this, he associated a 2-complex to the presentation. The monoid then has finite derivation type if, modulo the action of the free monoid ring, the 1-dimensional homotopy of this complex is finitely generated. Cremanns and Otto showed that finite derivation type implies the homological finiteness c...