Skip to main content

Quantum Hodge symmetries of Kahler manifolds

Posted in
Speaker: 
Alexander Goncharov
Organiser(s): 
Yale University/MPIM
Date: 
Tue, 2018-07-03 14:00 - 15:00
Location: 
MPIM Seminar Room

The product of two harmonic forms on a Riemannian manifold X is usually not harmonic. Instead,
there is an A-infinity algebra structure on the space of harmonic forms, which is quasiisomorphic
to the cohomology algebra of  X.

On a Kahler manifold Y the higher products above vanish.  We show that instead
a new phenomenon appears: the Tannakain Galois group of the category real mixed Hodge structures
acts by A-infinity automorphisms of the cohomology algebra of X.

Both constructions have a quantum = higher genus generalization:
For a Riemannian X, the A-infinity product extends to a quantum A-infinity algebra structure, and
for a Kahler manifold Y the real Hodge Galois group acts by quantum A-infinity automorphisms
of the cohomology algebra of Y.

There are similar further generalizations of these constructions when  for the Ext's between local
systems on X / semisimple local systems on Y.
 

© MPI f. Mathematik, Bonn Impressum & Datenschutz
-A A +A