5,806 reputation
11948
bio website dm.unipi.it/~martelli
location Pisa (Italy)
age 41
visits member for 4 years, 7 months
seen 12 hours ago
Assistant professor (ricercatore) at Math Dept (University of Pisa)

Dec
9
revised Does there always exist a sequence of handle moves between handle decompositions that does not increase index? (+ ref. request)
added 3 characters in body
Dec
9
revised Does there always exist a sequence of handle moves between handle decompositions that does not increase index? (+ ref. request)
fix
Dec
9
answered Does there always exist a sequence of handle moves between handle decompositions that does not increase index? (+ ref. request)
Dec
3
comment Can knot diagrams be monotonically simplified using under moves?
As suggested by Marco, this knot can be fully simplified via level moves, see zanellati.it/knot/Satellite_knot.pdf I just got this information from the author of the program who is following this page, so drawings of more complicated unknots are welcome :-) It would be interesting to try one more additional doubling as suggested by Joel...
Nov
28
awarded  Nice Answer
Nov
24
answered Additivity of simplicial volume
Nov
4
comment Examples of Einstein four-manifolds of negative sectional curvature
using Dehn filling on cusped hyperbolic manifolds (see the papers of Anderson and Bamler) you can construct plenty of manifolds that admit both Einstein and non-positive sectional curvature metrics, but not simultaneously as far as I understand.
Nov
4
comment Can knot diagrams be monotonically simplified using under moves?
I don't know (I still haven't seen the program running), but if you perform the diagram connected sum I suppose it simplifies the knot exactly as before. One should try some hard version of the trefoil knot...
Nov
4
revised Can knot diagrams be monotonically simplified using under moves?
picture
Nov
4
answered Can knot diagrams be monotonically simplified using under moves?
Oct
10
awarded  Good Answer
Sep
30
awarded  Explainer
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