ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

6. Topology

1991 MS Classification: 58-XX Millionshikov, Dmitri V., Moscow State University, Russia Krichever-Novikov algebras I. Krichever and S. Novikov, introducing their approach to string theory considered some algebro-geometric objects connected with Riemann surfaces. The most important ones are Krichever–Novikov algebras — natural generalisations of Virasoro algebra. Suppose Γ is a nondegenerate algebraic curve of genus g with two fixed generic points P_{±}; then a Krichever–Novikov algebra is defined the one-dimensional central extension of the algebra L^{Γ}(P_{±}) of meromorphic vector fields on Γ that are holomorphic outside P_{±}. Novikov’s conjecture (1987): dim H^{2}(L^{Γ}(P_{±}), ℂ) = 2g +1. In 1989 B. Feigin proposed some spectral sequences for computing of this cohomology, but without any explicit provement. A new approach for computing of H^{∗}(L^{Γ}(P_{±}), ℂ) is proposed.