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SUMMARY:Branched covers of quasipositive links and L-spaces - Steven Boyer
  (UQAM - Université du Québec à Montréal)
DTSTART:20170202T100000Z
DTEND:20170202T110000Z
UID:TALK70556@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:<span>         Co-authors: Michel Boileau 		(Universit&eacute\
 ; Aix-Marseille)\, Cameron McA. Gordon 		(University of Texas at Austin)  
       <br></span><span>&nbsp\;<br>We show that if L is an oriented non-tri
 vial strongly quasipositive link  or an oriented quasipositive link which 
 does not bound a smooth planar  surface in the 4-ball\, then the Alexander
  polynomial and signature  function of L determine an integer n(L) such th
 at \\Sigma_n(L)\, the  n-fold cyclic cover of S^3 branched over L\, is not
  an L-space for n >  n(L). If K is a strongly quasipositive knot with moni
 c Alexander  polynomial such as an L-space knot\, we show that \\Sigma_n(K
 ) is not an  L-space for n \\geq 6 and that the Alexander polynomial of K 
 is a  non-trivial product of cyclotomic polynomials if \\Sigma_n(K) is an 
  L-space for some n = 2\, 3\, 4\, 5. Our results allow us to calculate the
   smooth and topological 4-ball genera of\, for instance\, quasi-alternati
 ng  oriented quasipositive links. They also allow us to classify strongly 
  quasipositive 3-strand pretzel knots.&nbsp\;</span>
LOCATION:Seminar Room 1\, Newton Institute
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