# Tyson Ritter: Acyclic embeddings of open Riemann surfaces into new examples of elliptic manifolds

Source: Complex analysis seminar

Title: Acyclic embeddings of open Riemann surfaces into new examples of elliptic manifolds.

Abstract: In complex geometry a manifold is Stein if there are, in a certain sense, "many" holomorphic maps from the manifold into C^n. While this has long been well understood, a fruitful definition of the dual notion has until recently been elusive. In Oka theory, a manifold is Oka if it satisfies several equivalent definitions, each stating that the manifold has "many" holomorphic maps into it from C^n. Related to this is the geometric condition of ellipticity, due to Gromov, who showed that it implies a complex manifold is Oka. We present contributions to three open questions involving elliptic and Oka manifolds. We show that affine quotients of C^n are elliptic, and combine this with an example of Margulis to construct new elliptic manifolds of interesting homotopy types. It follows that every open Riemann surface properly acyclically embeds into an elliptic manifold, extending an earlier result for open Riemann surfaces with abelian fundamental group.

Seminar bo v predavalnici 3.06 na Jadranski 21. Vljudno vabljeni!

Vodji seminarja

Josip Globevnik in Franc Forstneric