Branched covers of quasipositive links and L-spaces
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About this item
| Description: |
Boyer, S (UQAM - Université du Québec à Montréal)
Thursday 2nd February 2017 - 10:00 to 11:00 |
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| Created: | 2017-02-14 09:41 |
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| Collection: | Homology theories in low dimensional topology |
| Publisher: | Isaac Newton Institute |
| Copyright: | Boyer, S |
| Language: | eng (English) |
| Distribution: |
World
(downloadable)
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| Explicit content: | No |
| Aspect Ratio: | 16:9 |
| Screencast: | No |
| Bumper: | UCS Default |
| Trailer: | UCS Default |
| 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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