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SUMMARY:Pin(2)-equivariant Floer homology and homology cobordism - Matthew
  Stoffregen (University of California\, Los Angeles)
DTSTART:20170203T100000Z
DTEND:20170203T110000Z
UID:TALK70596@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We review Manolescu&#39\;s construction of the <span><span><sp
 an><img alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/H
 TML-CSS/TeX/png/Main/Regular/141/0050.png"><img alt="" src="http://www-old
 .newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/141/0
 069.png"><img alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/f
 onts/HTML-CSS/TeX/png/Main/Regular/141/006E.png"></span><img alt="" src="h
 ttp://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Main/
 Regular/141/0028.png"><img alt="" src="http://www-old.newton.ac.uk/js/Math
 Jax/current/fonts/HTML-CSS/TeX/png/Main/Regular/141/0032.png"><img alt="" 
 src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png
 /Main/Regular/141/0029.png"></span>&nbsp\;</span>-equivariant  Seiberg-Wit
 ten Floer stable homotopy type\, and apply it to the study of  the 3-dimen
 sional homology cobordism group.  We introduce the `local  equivalence&#39
 \; group\, and construct a homomorphism from the homology  cobordism group
  to the local equivalence group.  We then apply  Manolescu&#39\;s Floer ho
 motopy type to obstruct cobordisms between Seifert  spaces.  In particular
 \, we show the existence of integral homology  spheres not homology cobord
 ant to any Seifert space.  We also introduce  connected Floer homology\, a
 n invariant of homology cobordism taking  values in isomorphism classes of
  modules.
LOCATION:Seminar Room 1\, Newton Institute
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