Manchester Geometry Seminar 1999/2000
Extra session. 5 November 1999, Friday. Maths Tower, N6. 3 p.m.
Groups of Polynomial Transformations
and Applications
Victor Buchstaber
(Moscow State University and the Steklov Mathematical Institute)
buchstab@mech.math.msu.su
The talk is devoted to a remarkable noncommutative algebraic group
structures on n-dimensional Euclidean spaces with a canonical
deformation to the standard commutative addition.
We will discuss the applications to the geometry of symplectic
nilmanifolds and to some fundamental problems of algebraic topology.
Main topics:
-
Nilpotent group structures, defined by groups of polynomial
transformations of a line.
-
Cocompact lattices and nilmanifolds.
-
Differential graded algebras of left invariant differential
forms on some nilmanifolds.
-
Nonformal symplectic nilmanifolds and applications.
-
Massey products structures on cohomology ring of nilmanifolds
and stable homotopy groups of spheres.
All necessary definitions will be given. The talk will be
accessible to a broad mathematical audience.