Seminar in Real and Complex Geometry

Thursday, December 6, 2018, 16:00-18:00, Schreiber building, room 209

Shachar Carmeli (Weizmann Institute)

Ambidexterity in Chromatic Homotopy Theory


Poincaré duality provides an isomorphism between the homology and cohomology of a compact manifold, up to a shift. For \pi-finite spaces, i.e. spaces with finitely many non-zero homotopy groups, all of which are finite, there is a similar duality only for Q-coefficients, but no such duality exists with F_p coefficients. However, as shown by Michael Hopkins and Jacob Lurie, there is a duality between the homology and cohomology of \pi-finite spaces with coefficients in some extra-ordinary cohomology theories called Morava K-theories. This property of Morava K-theory is called ambidexterity. I will explain what is ambidexterity and some of its consequences.