{"id":908,"date":"2015-10-13T19:20:44","date_gmt":"2015-10-13T23:20:44","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/boyland\/?page_id=908"},"modified":"2026-03-19T08:10:28","modified_gmt":"2026-03-19T12:10:28","slug":"vladimir-chernov","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/boyland\/vladimir-chernov\/","title":{"rendered":"Vladimir Chernov"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h1 class=\"wp-block-heading\">Vladimir Chernov<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">Linking, causality and smooth structures on spacetimes (based on joint work with Stefan Nemirovski).<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Abstract:\u00a0 Globally hyperbolic spacetimes form probably the most important class of spacetimes. Low conjecture and the Legendrian Low conjecture formulated by Nat\\&#8217;ario 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.<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">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&#8217;s problem list communicated by Penrose.<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">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.<\/p>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":146,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-908","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/908","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/users\/146"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/comments?post=908"}],"version-history":[{"count":2,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/908\/revisions"}],"predecessor-version":[{"id":4015,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/908\/revisions\/4015"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/media?parent=908"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}