Elliptic and Krichever formal group laws

The talk presents our main results on elliptic and Krichever formal group laws and their applications to
analysis on manifolds. The general elliptic formal group law is dened by the geometric group structure on the ellipic curve in the
general Weierstrass model with arithmetic Tate uniformization.
We present the explicit form of this formal group law and the differential equations that define its exponential.
Each formal group law defines a Hirzebruch genus of stably complex manifolds.
We obtain form Tate's
results that the Hirzebruch genus corresponding to the general elliptic formal group law is integer over the
ring of parameters. We name this genus the general elliptic genus and discribe it explicitly.
We introduce the formal group law such that its exponential denes the famous Krichever genus and
name it the Krichever formal group law. We give the explicit form of this group law and conditions necessary
and sucient for it to be an elliptic formal group law. This conditions correspond to four cases, two of which
lead to the two-parametric Todd genus and the Ochanine-Witten elliptic genus, and the other two are new.
All four cases give Hirzebrugh genera rigid on S^1-equivariant SU-manifolds (S^1-equivariant Calabi-Yau manifolds).
The main results presented in the talk are obtained in collaboration with V.M.Buchstaber.
All needed denitions will be given during the talk.