Date & Time: Wednesday, September 03, 2014, 16:00-17:00.
Venue: Ramanujan Hall
Speaker: Ramesh K, IIT Bombay
Title: Smooth Structures on Hyperbolic Manifolds
Abstract: We discuss the method of detecting exotic structures on $\mathbb{K}$-hyperbolic manifolds given by F.T. Farrell, L.E. Jones and C.S. Aravinda, where $\mathbb{K}=\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$ or $\mathbb{O}.$ We also discuss the following question raised by F.T. Farrell and C.S. Aravinda (2004).
Question: For each division algebra $\mathbb{K}$ over the reals and each integer $n\geq 2$ ($n = 2$ when $\mathbb{K}=\mathbb{O}$), does there exist a closed negatively curved Riemannian manifold $M^{dn}$(where $d=\dim_{\mathbb{R}} \mathbb{K}$) which is homeomorphic but not diffeomorphic to a $\mathbb{K}$-hyperbolic manifold?
Finally, we give some observations on the work of F.T. Farrell, L.E. Jones, C.S. Aravinda and C.T.C. Wall.