bio | website | dm.unipi.it/~martelli |
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location | Pisa (Italy) | |
age | 41 | |
visits | member for | 4 years, 10 months |
seen | 11 hours ago | |
stats | profile views | 3,458 |
Associate professor in geometry (Pisa, Italy)
Feb 5 |
awarded | Good Answer |
Jan 23 |
comment |
Fox re-imbedding theorem in dimension four
More generally, which re-imbedding techniques do we know? If I have a 3-manifold in S^4, how can I modify its embedding so that it is not isotopic to the previous one? |
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?
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