Teichmuller spaces of negatively curved metrics

Schedule:2.21~5.13 (Tues. /Thurs. ) 9:50-11:25
Venue:近春西楼第一会议室 Conference Room 1

课程描述 Description

The Teichmuller space of all negatively curved metrics for a high dimensional closed manifold M is defined to be the quotient of the space of all negatively curved metrics on M by the group of all self-diffeomorphisms of M which are homotopic to the identity. Different from the 2 dimensional case, these Teichmuller spaces for higher dimensional manifolds are not contractible in general. This course is aim at introducing the homotopy theory for Teichmuller spaces of negatively curved metrics on high dimensional manifolds and some related open problems.

讲义 Notes:Feb.22/24[PDF] Mar.1/3[PDF] Mar.8/10[PDF] Mar.15/17[PDF] Mar.22/24[PDF] Mar.29/31[PDF] Apr.7[PDF]

Apr.12/14[PDF] Apr.19/21[PDF] Apr.26/28&May.7[PDF] MAY.10/12[PDF]

预备知识 Prerequisites

Elementary algebraic topology, differentiable topology and differential geometry

参考资料 References

1. F. Thomas Farrell and Pedro Ontaneda. The Teichmuller space of pinched negatively curved metrics on a hyperbolic manifold is not contractible. Ann. of Math. (2), 170(1):45-65, 2009.

2. F. T. Farrell. Bundles with extra geometric or dynamic structure. In The legacy of Bernhard Riemann after one hundred and fifty years. Vol. I, volume 35 of Adv. Lect. Math. (ALM), pages 223{250. Int. Press, Somerville, MA, 2016.