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SUMMARY:Topology Seminar: Homotopically rigid Sullivan algebras and their 
 applications
DTSTART:20171003T101500
DTEND:20171003T111000
DTSTAMP:20260429T114600Z
UID:b540e98758e12b8503a312da05ac2353a883ef2925c8769101cebf20
CATEGORIES:Conferences - Seminars
DESCRIPTION:David Méndez (EPFL & Universidad de Málaga)\nAbstract: The g
 roup of homotopy self-equivalences of a space is rarely trivial. Kahn was 
 the first to obtain an example of one such space with non-trivial rational
  homology in the seventies. Later\, Arkowitz and Lupton came across an exa
 mple of a Sullivan algebra (equivalently\, a rational homotopy type) with 
 trivial homotopy self-equivalences. This algebra was used by Costoya and V
 iruel to solve Kahn's group realisability problem for finite groups\, thus
  obtaining for any finite group G a rational space X whose group of homoto
 py self-equivalences is isomorphic to G. This construction also provide a 
 way to obtain an infinite amount of homotopically rigid spaces. However\, 
 they all share their level of connectivity with the example of Arkowitz an
 d Lupton.\n\nThe objective of this talk is to illustrate that\n(i) Homotop
 ically rigid spaces are not as rare as they were though to be. We are able
  to obtain an infinite family of homotopically rigid spaces\, showing a le
 vel of connectivity as high as desired. \n(ii) Building blocks other than
  the example of Arkowitz and Lupton can be used to solve Kahn's realisabil
 ity problem. \nWe can also apply the obtained results to differential geo
 metry by enlarging the class of inflexible manifolds existing in literatur
 e and building new examples of strongly chiral manifolds.\n\nReference:\nC
 . Costoya\, D. Méndez\, A. Viruel\, Homotopically rigid Sullivan algebra
 s and their applications\, arXiv:1701.03705 [math.AT].
LOCATION:CM 0 12 https://plan.epfl.ch/?room=CM012
STATUS:CONFIRMED
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