6 papers
A note on weight systems which are quantum states
Carlo Collari
A result of Corfield, Sati, and Schreiber asserts that -weight systems associated to the defining representation are quantum states. In this short note we extend t…
Monotone cohomologies and oriented matchings
Luigi Caputi, Daniele Celoria, Carlo Collari
In this paper, we extend the definition of cohomology associated to monotone graph properties, to encompass twisted functor coefficients. We introduce oriented matchings on graphs,…
A note on the weak splitting number
Alberto Cavallo, Carlo Collari, Anthony Conway
The weak splitting number of a link is the minimal number of crossing changes needed to turn into a split union of knots. We describe conditions under which certai…
Slice-torus concordance invariants and Whitehead doubles of links
Alberto Cavallo, Carlo Collari
In the present paper we extend the definition of slice-torus invariant to links. We prove a few properties of the newly-defined slice-torus link invariants: the behaviour under cro…
Transverse link invariants from the deformations of Khovanov -homology
Carlo Collari
In this paper we will make use of the Mackaay-Vaz approach to the universal -homology to define a family of cycles (called -invariants) which are transverse b…
Symmetric union diagrams and refined spin models
Carlo Collari, Paolo Lisca
An open question akin to the slice-ribbon conjecture asks whether every ribbon knot can be represented as a symmetric union. Next to this basic existence question sits the question…