205 reputation
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age 25
visits member for 3 years, 8 months
seen Nov 21 at 17:50

I'm interested in the great amount of mathematics involved in the study of low-dimensional manifolds, above all the interaction between topology, geometry and algebra (and physics?).


Nov
10
awarded  Yearling
Sep
24
awarded  Autobiographer
Jan
7
awarded  Nice Question
Dec
24
awarded  Critic
Oct
12
awarded  Supporter
Oct
12
accepted Why is the mapping class group of hyperbolic manifolds finite?
May
30
asked Why is the mapping class group of hyperbolic manifolds finite?
Apr
25
comment Heegaard splitting, equivalent homeomorphisms, mapping class group of genus n-torus
wow, this is what I was looking for! Thank you sooooo much!!
Apr
23
comment Heegaard splitting, equivalent homeomorphisms, mapping class group of genus n-torus
[continued] What can we say about the two resulting manifolds? Even if we take f and g in the same double coset, they do not in general extend to automorphisms of the manifolds, so we don't get an isomorphism between them. Moreover, if they give the same manifold, do they give equivalent splittings? This is the kind of questions I'm thinking about.
Apr
23
comment Heegaard splitting, equivalent homeomorphisms, mapping class group of genus n-torus
I didn't find anything at that page...anyway I already knew that book, so I think you are referring to the article of Birman (maybe we have different page numberings). The point is I'm not satisfied with this :) I mean: by Birman, we know that if a manifold admits two equivalent splittings, than they are obtain from gluing maps which are in the same double coset. But what about the converse? Suppose we are given two genus g handlebodies and we want to glue them along their boundaries to obtain a 3-manifold, and we use two different maps, say $f$ and $g$.
Apr
20
comment Heegaard splitting, equivalent homeomorphisms, mapping class group of genus n-torus
Hi Maxime, can you please give me a reference for the first part of your answer ("You obtain the same Heegaard splitting iff your homeomorphisms are in the same double coset H\M/H where H is the subgroup of mapping classes that extend to the handlebody.") Moreover, I can't catch which is the relation between saying that two splitting give the same manifold (up to homeomorphism) and saying that two splitting are equivalent splittings for the same manifold. Someone can help? thanks in advance
Mar
26
asked Splitting lemma for non abelian groups and mapping class group
Mar
24
awarded  Scholar
Mar
24
comment Why is Casson's invariant worth studying?
ok thank you, and sorry..it's my first question on MathOverflow
Mar
24
accepted Why is Casson's invariant worth studying?
Mar
22
comment Why is Casson's invariant worth studying?
Wow thank you so much..you give me lots of things to think about! thank you again for your answer!
Mar
17
awarded  Student
Mar
17
asked Why is Casson's invariant worth studying?