Nous donnons une nouvelle construction cohomologique du cœur de l'invariant de Casson et nous donnons un nouveau calcul de ses valeurs sur les générateurs du sous- groupe de Johnson du mapping class group.
For every rational homology 3-sphere with H₁(M,ℤ) = (ℤ/2ℤ)ⁿ we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring) such that the evaluation of this invariant at any odd root of unity provides the SO(3) Witten-Reshetikhin-Turaev invariant at this root, and at any even root of unity the SU(2) quantum invariant. Moreover, this unified invariant splits into a sum of the refined unified invariants dominating spin and cohomological refinements of...
This paper is a concise introduction to virtual knot theory, coupled with a list of research problems in this field.