Localized Landweber-Novikov operations on generalized cohomology

par Kirill Zaynullin (University of Ottawa)

jeudi 14 mars 2019, 14:00 → 15:00 Europe/Paris

112 (bât. Braconnier)

Cohomological operations on generalized cohomology theories   (e.g. Steenrod, Adams, Landweber-Novikov) have been extensively  studied during the past decade (Brosnan, Levine, Merkurjev, Vishik).   They turned out to be extremely useful in generating interesting   rational cycles in higher codimension (e.g. idempotents or $0$-cycles  on twisted flag varieties), hence, in computing various geometric  invariants of torsors (incompressibility, canonical dimension,  torsion, motivic decomposition type, etc.).

In the present talk, we explain how to extend the Landweber-Novikov  operations on algebraic cobordism to the setup of equivariant   generalized cohomology theories via the localization techniques of  Kostant-Kumar. The operations we obtain we call localized operations.  These operations can be viewed as operations on global sections of the  so called structure sheaves on moment graphs (corresponding to  arbitrary Coxeter groups). They satisfy several natural properties,  e.g. they commute with characteristic map and restrict to usual  Landweber-Novikov operations.