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SUMMARY:Null surgery on knots in L-spaces - Yi Ni (CALTECH (California Ins
 titute of Technology))
DTSTART:20170201T090000Z
DTEND:20170201T100000Z
UID:TALK70532@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Co-author: Faramarz Vafaee 		(Caltech)        <br><span>&nbsp\
 ;<br>Let <span><img alt="" src="http://www-old.newton.ac.uk/js/MathJax/cur
 rent/fonts/HTML-CSS/TeX/png/Math/Italic/141/004B.png">&nbsp\;</span> be a 
 knot in a rational homology sphere <span><img alt="" src="http://www-old.n
 ewton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Math/Italic/141/0059
 .png">&nbsp\;</span>. Then there is a unique surgery on <span><img alt="" 
 src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png
 /Math/Italic/141/004B.png">&nbsp\;</span> which results a manifold with <s
 pan><span><span><span><img alt="" src="http://www-old.newton.ac.uk/js/Math
 Jax/current/fonts/HTML-CSS/TeX/png/Math/Italic/141/0062.png">&nbsp\;</span
 ><span><img alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fon
 ts/HTML-CSS/TeX/png/Main/Regular/100/0031.png">&nbsp\;</span></span><img a
 lt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/T
 eX/png/Main/Regular/141/003E.png"><img alt="" src="http://www-old.newton.a
 c.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/141/0030.png">
 </span>&nbsp\;</span>. We call this surgery the null surgery. When <span><
 img alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-
 CSS/TeX/png/Math/Italic/141/0059.png">&nbsp\;</span>  is an L-space\, the 
 null surgery remembers the information about the  genus and fiberedness of
  the knot. A special case of our theorem is that  if the resulting manifol
 d is <span><span><span><span><img alt="" src="http://www-old.newton.ac.uk/
 js/MathJax/current/fonts/HTML-CSS/TeX/png/Math/Italic/141/0053.png">&nbsp\
 ;</span><span><img alt="" src="http://www-old.newton.ac.uk/js/MathJax/curr
 ent/fonts/HTML-CSS/TeX/png/Main/Regular/100/0031.png">&nbsp\;</span></span
 ><img alt="" src="http://www-old.newton.ac.uk/js/MathJax/current/fonts/HTM
 L-CSS/TeX/png/Main/Regular/141/00D7.png"><span><span><img alt="" src="http
 ://www-old.newton.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Math/Ita
 lic/141/0053.png">&nbsp\;</span><span><img alt="" src="http://www-old.newt
 on.ac.uk/js/MathJax/current/fonts/HTML-CSS/TeX/png/Main/Regular/100/0032.p
 ng">&nbsp\;</span></span></span>&nbsp\;</span>\, then the dual knot is a s
 pherical braid. This is joint work with Faramarz Vafaee.</span>
LOCATION:Seminar Room 1\, Newton Institute
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