bio | website | www-fourier.ujf-grenoble.fr/… |
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location | Grenoble, France | |
age | 29 | |
visits | member for | 3 years, 10 months |
seen | Mar 31 at 22:52 | |
stats | profile views | 793 |
Maître de conférences at Université de Grenoble (France)
Mar 24 |
awarded | Nice Question |
Sep 30 |
accepted | Fibered knot with periodic homological monodromy |
Sep 15 |
awarded | Yearling |
Jun 25 |
awarded | Excavator |
Jun 25 |
awarded | Suffrage |
Apr 24 |
revised |
Fibered knot with periodic homological monodromy
added 198 characters in body |
Apr 24 |
revised |
Fibered knot with periodic homological monodromy
added 70 characters in body |
Apr 24 |
comment |
Fibered knot with periodic homological monodromy
Thanks for your answer. Now I realize that Morton's construction (H. R. MORTON, 'Fibred knots with a given Alexander polynomial', Enseign. Math. 31 (1983), 205-222) actually gives counter-examples: Morton constructs infinitely many distinct fibered knots with prescribed Alexander polynomial (actually he starts from Burde's knots and twists). If we take his construction for a cyclotomic Alexander polynomial, then the homological monodromy has to be periodic (since diagonalizable), but infinitely many of Morton's knots will have pseudo-Anosov monodromy. |
Apr 23 |
asked | Fibered knot with periodic homological monodromy |
Apr 23 |
comment |
Genus one fibered links
Thanks Ken. Along the same line, one can start from a trefoil and plumb a Hopf band. This can be done in several ways, depending on a joice of a segment on the punctured torus, that is, a rational number. The monodromy in this case is the product of a matrix of trace 1 and a matrix of trace 2, and we can obtain many conjugacy classes in this way (I think at least one per trace). If we start from a figure-eight, it works in the same way, except that we obtain the product of a matrix of trace 3 with a matrix of trace 2. |
Apr 11 |
comment |
Genus one fibered links
Thanks! The Stallings twist seems a good idea, I will think about it. |
Apr 11 |
revised |
Genus one fibered links
added 10 characters in body |
Apr 11 |
revised |
Genus one fibered links
added 1 characters in body |
Apr 11 |
asked | Genus one fibered links |
Mar 30 |
awarded | Necromancer |
Nov 3 |
awarded | Notable Question |
Sep 21 |
answered | closed dual of vector fields |
Sep 17 |
awarded | Yearling |
Jun 18 |
revised |
Pseudonyms of famous mathematicians
added 15 characters in body |
Jun 11 |
comment |
What information can one recover from the induced map on homology?
Well, I was assuming that you have an homeomorphism. Then the thing is that pseudo-Anosov maps minimize the entropy in their isotopy class, so that the bound on the entropy in the main theorem of Birman et al is a fortiori valid for any homeo. But I have no idea about the non-homeo case. |