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SUMMARY:Non-Hausdorff Manifolds: Trick or Treat? - David O'Connell\, Okina
 wa Institute of Science and Technology
DTSTART:20231031T160000Z
DTEND:20231031T170000Z
UID:TALK204379@talks.cam.ac.uk
CONTACT:Alexis Marchand
DESCRIPTION:In this talk we will introduce various aspects of the weird wo
 rld of non-Hausdorff manifolds. Typically the Hausdorff property is includ
 ed in the definition of a manifold for technical convenience. The alternat
 ive is somewhat daunting: without the Hausdorff property we do not have ac
 cess to partitions of unity in their full generality\, and thus various st
 ructures may or may not exist in the non-Hausdorff case.  However\, as we 
 will see\, certain topological representations allow us to circumvent this
  issue and recreate differential geometry without the need of arbitrarily-
 existent partitions of unity. To illustrate this idea\, we will start from
  the topology of non-Hausdorff manifolds and then slowly introduce more an
 d more structure of various interest. I will try to keep the talk self-con
 tained\, though I will need to assume familiarity with the basics of diffe
 rential geometry and point-set topology.
LOCATION:MR3
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