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Causality in spacetimes and Legendrian linking
by
Vladimir Chernov
Dartmouth College
Coauthors: Stefan Nemirovski
Two points in a spacetime X are said to be causally related if one can get from one to the other travelling at less or equal than light speed. Low conecjture and the Legendrian Low conjecture formulated by Natário and Tod say that for nice 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.
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.
If time permits we discuss which of the smooth 4-manifolds admit a globally hyperbolic Lorentz metric, generalizing the results of Newman and Clarke.
Date received: March 28, 2011
Copyright © 2011 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbcc-06.