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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240509T153000
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URL:https://uwaterloo.ca/pure-mathematics/events/strange-manifolds-small-co
 homotopy-and-baire-classes
SUMMARY:Strange manifolds\, small cohomotopy and Baire classes
CLASS:PUBLIC
DESCRIPTION:Alex Chirvasitu\, University at Buffalo\n\nPr¨ufer surfaces ar
 e non-metrizable separable 2-manifolds originally\ndefined by Calabi and R
 osenlicht by doubling the upper half-plane\nalong a continuum’s worth of
  real-line boundary components. The\nconstruction and variations on it hav
 e since been studied by Gabard\,\nBaillif and many others for the purpose 
 of probing the pathologies of\nnon-paracompact manifolds. The fundamental 
 groups of such surfaces and\nhigher-dimensional cousins are known to be (e
 ssentially) free on the\nsets S of connected boundary components\, so thei
 r first cohomotopy\ngroups (i.e. sets of homotopy classes of continuous ma
 ps to rather\nthan from the circle) are identifiable with maps from S to t
 he\nintegers. Which functions S → Z arise in this manner is a natural\nq
 uestion\, with (perhaps) a surprising answer. The goal will be to\ndiscuss
  that problem\, but the manifolds themselves might provide some\nentertain
 ment value on their own.\n\nMC5417
DTSTAMP:20260505T133052Z
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