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SUMMARY:Generalized Bestvina-Brady groups and their applications - Ian Lea
 ry (University of Southampton)
DTSTART:20170621T080000Z
DTEND:20170621T090000Z
UID:TALK73014@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>Co-authors: Robert Kropholler		(Tufts University)\, Igna
 t Soroko		(University of Oklahoma)        <br></span><span><br>In the 1990
 &#39\;s Bestvina and Brady used Morse theory to exhibit (as subgroups of r
 ight-angled Artin groups) the first examples of groups that are <span><img
  alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS
 /TeX/png/Math/Italic/141/0046.png"><img alt="" src="http://www-old.newton.
 ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Math/Italic/141/0050.png">
 </span>   but not finitely presented.   <br></span><span><br>The speaker h
 as generalized this construction\, via branched coverings\, to construct c
 ontinuously many groups of type <span><img alt="" src="http://www-old.newt
 on.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Math/Italic/141/0046.pn
 g"><img alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/H
 TML-CSS/TeX/png/Math/Italic/141/0050.png"></span>  \, including groups of 
 type FP that do not embed in any finitely presented group.   <br></span><s
 pan><br>I shall discuss the construction and some applications\, including
  the theorem that every countable group embeds in a group of type <span><i
 mg alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-C
 SS/TeX/png/Math/Italic/141/0046.png"><span><img alt="" src="http://www-old
 .newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Math/Italic/141/00
 50.png"><img alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fo
 nts/HTML-CSS/TeX/png/Main/Regular/100/0032.png"></span></span>   and the c
 onstruction of continuously many quasi-isometry classes of acyclic 4-manif
 olds admitting free\, cocompact\, properly discontinuous discrete group ac
 tion (the latter joint with Robert Kropholler and Ignat Soroko).   <br></s
 pan><br>Related Links<ul><li><a target="_blank" rel="nofollow" href="http:
 //www-old.newton.ac.uk/cgi/https%3A%2F%2Farxiv.org%2Fabs%2F1512.06609">htt
 ps://arxiv.org/abs/1512.06609</a> - Archive link to preprint with main res
 ult</li><li><a target="_blank" rel="nofollow" href="http://www-old.newton.
 ac.uk/cgi/https%3A%2F%2Farxiv.org%2Fabs%2F1610.05813">https://arxiv.org/ab
 s/1610.05813</a> - Archive link to preprint on subgroups of <span><img alt
 ="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX
 /png/Math/Italic/141/0046.png"><span><img alt="" src="http://www-old.newto
 n.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Math/Italic/141/0050.png
 "><img alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HT
 ML-CSS/TeX/png/Main/Regular/100/0032.png"></span></span>   groups</li></ul
 >
LOCATION:Seminar Room 1\, Newton Institute
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