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SUMMARY:Corey Bregman (Brandeis)
DTSTART:20200616T150000Z
DTEND:20200616T153000Z
DTSTAMP:20260423T021049Z
UID:GaTO/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GaTO/15/">Is
 otopy and equivalence of knots in three-manifolds</a>\nby Corey Bregman (B
 randeis) as part of Geometry and topology online\n\n\nAbstract\nIt is a we
 ll-known fact that the notions of\n<i>(ambient) isotopy</i> and <i>equival
 ence</i> coincide for\nknots in \\(S^3\\).  This is because all orientatio
 n-preserving\nhomeomorphisms of \\(S^3\\) are isotopic to the identity.  I
 n\nthis talk\, we compare the notions of equivalence and isotopy\nfor knot
 s in more general three-manifolds.\n\nWe show that the mapping class group
  of a three-manifold\n"sees" all the isotopy classes of knots\; that is\, 
 if an\norientation-preserving homeomorphism fixes every isotopy\nclass\, t
 hen it is isotopic to the identity.  In the case of\n\\(S^1 \\times S^2\\)
  we give infinitely many examples of knots\nwhose isotopy classes are chan
 ged by the Gluck twist.  Along\nthe way we prove that every three-manifold
  group satisfies\nGrossman's Property A.\n\nThis is joint work with Paolo 
 Aceto\, Christopher Davis\,\nJungHwan Park\, and Arunima Ray.\n
LOCATION:https://researchseminars.org/talk/GaTO/15/
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