1,148 reputation
920
bio website www-fourier.ujf-grenoble.fr/…
location Grenoble, France
age 29
visits member for 3 years, 10 months
seen Mar 31 at 22:52

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
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Apr
24
revised Fibered knot with periodic homological monodromy
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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
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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
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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.