Title: Linking, causality and smooth structures on spacetimes
Speaker: Vladimir Chernov, Dartmouth College
Abstract: Globally hyperbolic spacetimes form probably the most important class of spacetimes. Low conjecture and the Legendrian Low conjecture formulated by Natario and Tod say that for many globally hyperbolic spacetimes X two events x,y in X are causally related if and only if the link of spheres S_x, S_y whose points are light rays passing through x and y is non-trivial in the contact manifold N of all light rays in X. This means that the causal relation between events can be reconstructed from the intersection of the light cones with a Cauchy surface of the spacetime.
We prove the Low and the Legendrian Low conjectures and show that similar statements are in fact true in almost all $4$-dimensional globally hyperbolic spacetimes. This also answers the question on Arnold's problem list communicated by Penrose.
We also show that on many 4-manifolds there is a unique smooth structure underlying a globally hyperbolic Lorentz metric, thus global hyperbolicity imposes censorship on the possible smooth structures on a spacetime. For instance, every contractible smooth 4-manifold admitting a globally hyperbolic Lorentz metric is diffeomorphic to the standard R^4. (based on joint work with Stefan Nemirovski).
Short bio: Vladimir Chernov is a researcher in contact geometry, Lorentz geometry and in low dimensional topology. His interests also include various aspects of general relativity. He is a professor at the Mathematics Department of Dartmouth College. Before that he had one year positions at University Zurich, MPIM Bonn, and ETH Zurich. He has graduated from University of California Riverside and Uppsala University Sweden. His advisor was Oleg Viro.