Скачать или смотреть Prof. Steven Boyer | Branched covers of quasipositive links and L-spaces

Speaker: Professor Steven Boyer (UQAM - Université du Québec à Montréal)
Date: 2nd Feb 2017 - 10:00 to 11:00
Venue: INI Seminar Room 1
Title: Branched covers of quasipositive links and L-spaces
Event: (HTLW02) 3-manifold workshop
Abstract: Co-authors: Michel Boileau
(Université Aix-Marseille), Cameron McA. Gordon
(University of Texas at Austin)
We show that if L is an oriented non-trivial 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 that \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 monic 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-alternating
oriented quasipositive links. They also allow us to classify strongly
quasipositive 3-strand pretzel knots.

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