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SUMMARY:Birman-Hilden theory for reducible 3-manifolds - Trent  Lucas (Bro
 wn University)
DTSTART:20240614T133000Z
DTEND:20240614T140000Z
UID:TALK217795@talks.cam.ac.uk
DESCRIPTION:For a manifold M\, we discuss its mapping class group Mod(M) =
  Homeo+(M)/isotopy.&nbsp\; Given a finite branched cover of manifolds M ->
  N\, one can lift mapping classes from N to M to obtain a (virtual) homomo
 rphism of mapping class groups.&nbsp\; A celebrated theorem of Birman-Hild
 en and MacLachlan-Harvey says that if M is a hyperbolic surface\, then thi
 s lifting map is injective for all regular covers.&nbsp\; Following a ques
 tion of Margalit-Winarski\, we show that this lifting map is not injective
  for many branched covers of reducible 3-manifolds\, and we study the kern
 el for the 3-manifold analog of the hyperelliptic involution.&nbsp\; In th
 is case\, the lifting map is closely related to symmetric outer automorphi
 sm groups of free products.
LOCATION:External
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