Title: Ricci flow on open 4-manifolds with positive isotropic curvature

Speaker: 黄红(Beijing Normal University)

Time: Sep 1,Thursday,2011,14:00-16:00pm

Venue: Room 1328 at BICMR, Resource Plaza, Peking University

Abstract：In this talk we will use Ricci flow with surgery to classify complete 4-manifolds (or orbifolds) with uniformly positive isotropic curvature and with bounded geometry.

As a simple case, let $X$ be a complete, connected 4-manifold with uniformly positive isotropic curvature, with bounded geometry and with no essential incompressible space form, then we can show that $X$ is diffeomorphic to $mathbb{S}^4$, or $mathbb{RP}^4$, or $mathbb{S}^3 imes mathbb{S}^1$, or $mathbb{S}^3widetilde{ imes} mathbb{S}^1$, or a possibly infinite connected sum of them. This extends work of Hamilton, Chen-Zhu and Chen-Tang-Zhu to the noncompact case. It is inspired by recent work of Bessi$grave{e}$res, Besson and Maillot.