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Saturday November 16, 2013, at UCLA A Day of Triangulations The day's program will be devoted to the history and solution of the century-old Triangulation of Manifolds Question: Is an arbitrary topological manifold triangulable, i.e. homeomorphic to a simplicial complex? The talks will highlight some key aspects of these developments which are linked with UCLA. 10:30 in Math Sciences 6620 (the Math Common Room): Coffee and greetings. All talks are in Math Sciences 6627. 11:00: Rob Kirby, UC Berkeley. The 1968 UCLA torus trick epiphany and PL triangulations of manifolds. 12-1:30 Lunch. (On your own. Plenty of options on campus and in Westwood.) 1:30: Bob Edwards, UCLA. Non-PL triangulations of manifolds exist. 2:45: Ron Stern, UCI (UCLA PhD 1973). Simplicial triangulations of high dimensional manifolds and the homology cobordism group of homology 3-spheres. 3:45: Refreshments in Math Sciences 6620. 4:15: Ciprian Manolescu, UCLA. Resolving the Triangulation Question in high dimensions: The non-existence of certain homology 3-spheres. 5:15: Speakers' Panel: Further Discussion, Reminiscences and Open Problems. 6:00: Buffet Dinner in Math Sciences 6620. Some Background and History: The first successful efforts on the Triangulation-of-Manifolds Question occurred in the 1920s when the 2-dimensional case was solved. Dimension 3 took another 30 years, finally being solved in the early 1950s. For the next 15 years the Conjecture remained open in dimensions >= 4, attracting ever more attention. In 1968 a breakthrough happened at UCLA when Rob Kirby discovered the torus trick. He then used it to crack open the higher dimensional cases for so-called combinatorial, i.e. PL triangulations, working with L. Siebenmann. Following the Kirby-Siebenmann work attention turned to the non-PL side of the Triangulation Question. The existence of non-PL triangulations was known to reduce to the Double Suspension Question for homology spheres: Is the 2-fold suspension of a homology sphere homeomorphic to a (genuine) sphere? This was solved affirmatively by Bob Edwards in 1974-76 for almost all cases. This provided non-PL triangulations for many manifolds which the Kirby-Siebenmann work had shown were not PL-triangulable. Jim Cannon completed the affirmative answer to the DSQ in 1977. Still there remained many manifolds for which the triangulation question remained open. In the mid-1970s a broad theory of triangulations was developed by Ron Stern with coauthor Dave Galewski, and independently by Takao Matumoto. This reduced the high-dimensional triangulation problem to a question of the existence of a special class of homology 3-spheres. In 1985 the first non-simplicially-triangulable manifolds were found in dimension four by Andrew Casson, following work of Mike Freedman. Finally in 2013 Ciprian Manolescu answered the Galewski-Stern-Matumoto question in the negative, thus showing the existence of non-triangulable manifolds in all dimensions five or higher. Web site: http://www.math.ucla.edu/topology/tc13.html =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- This message was sent to you via the Geometry List, which announces conferences in geometry and closely related areas to over 1200 mathematicians worldwide. At http://listserv.utk.edu/archives/geometry.html there are many functions available, including checking the archives since November 2005, changing your e-mail address or preferences, and joining/leaving the list. If you have problems that cannot be resolved at this website, send a message to [log in to unmask] Before sending an announcement, please carefully read the following. Any announcements that are *not* about conferences (e.g. those about jobs, journals, books, etc.) will be rejected by the moderator without comment. 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