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Faculty of Science Mathematics & Statistics
Faculty of Science

Mathematics & Statistics

Geometry and Topology Seminar, "Branched Covers of Quasipositive Links and L-Spaces", Steven Boyer

From September 14, 2017 15:30 until September 14, 2017 16:30
At HH/312

Steven Boyer, 
Département de mathématiques
Université du Québec à Montréal

Title: Branched Covers of Quasipositive Links and L-Spaces.

Abstract: We show that if L is an oriented strongly quasipositive link other than the trivial knot or a link whose Alexander polynomial is a positive power of (t-1), or a quasipositive link with non-zero smooth 4-ball genus, then the Alexander polynomial and signature function of L determine an integer n(L) ≥ 1 such that Σn(L), the n-fold cyclic cover of S3 branched over L, is not an L-space for n > n(L). If K is a strongly quasipositive knot with monic Alexander polynomial such as an L-space knot, we show that Σn(K) is not an L-space for n ≥ 6, and that the Alexander polynomial of K is a non-trivial product of cyclotomic polynomials if Σn(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- alternating quasipositive links. They also allow us to classify strongly quasipositive alternating links and strongly quasipositive alternating 3-strand pretzel links.    This is joint work with Michel Boileau and Cameron Gordon

 

 

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McMaster University - Faculty of Science

Mailing Address

Department of Mathematics & Statistics
McMaster University

Hamilton Hall, Room 218
1280 Main Street West
Hamilton, Ontario, Canada
L8S 4K1

Contact Information

Office Hours:
8:30 a.m. - 12:00 p.m.
1:00 p.m. - 4:30 p.m.
Telephone Inquiries:
+1 (905) 525-9140 ext.27034
Undergrad Email Inquiries:
undergrad@math.mcmaster.ca