5,551 reputation
11846
bio website dm.unipi.it/~martelli
location Pisa (Italy)
age 41
visits member for 4 years, 3 months
seen 2 hours ago
Assistant professor (ricercatore) at Math Dept (University of Pisa)

Aug
28
awarded  Popular Question
Aug
25
comment Is a generic closed orientable hyperbolic 3-manifold Haken?
are we sure that any configuration of tetrahedra appears with probability one? This does not hold for graphs (some graphs almost never appear as subgraphs of a random 4-valent graph).
Aug
24
comment Is a generic closed orientable hyperbolic 3-manifold Haken?
I see, if you fix the genus g then every manifold has Betti number at most g and a generic splitting has transverse lagrangians, hence it is a rational homology sphere. It would be nice to understand if a random manifold is Haken with this model.
Aug
24
comment Is a generic closed orientable hyperbolic 3-manifold Haken?
I think there is nothing really proved about gluing randomly tetrahedra, because it is very hard to control if the resulting object is a manifold. Moreover, we don't even know if the number of triangulations of S^3 with n tetrahedra grows exponentially with n or more. As far as we know, it might even be that a random triangulated 3-manifold is S^3 - although that sounds really unlikely.
Aug
24
comment Is a generic closed orientable hyperbolic 3-manifold Haken?
I would guess that in many reasonable models a random 3-manifold has arbitrarily high Betti number, just like a random surface has arbitrarily high genus.
Jul
22
revised Why are Witten-Reshetikhin-Turaev invariants expected to be integral?
added 19 characters in body
Jul
20
revised Why are Witten-Reshetikhin-Turaev invariants expected to be integral?
explain better
Jul
20
revised Why are Witten-Reshetikhin-Turaev invariants expected to be integral?
explain better
Jul
20
answered Why are Witten-Reshetikhin-Turaev invariants expected to be integral?
Jul
19
revised A question about Dehn surgery and Brieskorn homology 3-spheres
fix
Jul
19
answered A question about Dehn surgery and Brieskorn homology 3-spheres
Jul
18
comment What 3-manifolds can be obtained by gluing $ S^1 \times P $ and two copies of $S^1 \times D^2$
Yes (answer to second question) the number "p" in (p,q) is precisely that geometric intersection
Jul
18
comment What 3-manifolds can be obtained by gluing $ S^1 \times P $ and two copies of $S^1 \times D^2$
The gluing of a solid torus is parametrized simply by looking at the image (p,q) of the meridian: the image of the longitude is useless here, see en.wikipedia.org/wiki/Dehn_surgery You get: (0,1) is fiber-parallel, and (1,q) is non-exceptional.
Jul
17
answered What 3-manifolds can be obtained by gluing $ S^1 \times P $ and two copies of $S^1 \times D^2$
Jul
2
awarded  Curious
Jun
16
awarded  Notable Question
Jun
5
reviewed Approve suggested edit on unique enhancement for derived categories
May
20
awarded  Yearling
May
20
answered undergraduate handle decomposition. Reference
May
12
awarded  Nice Answer