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Apr
23 |
awarded | Popular Question |
Jun
24 |
comment |
riemannian length of an element of the fundamental group of a manifold
From another hand thanks for your answer but it doesn't answer the question because the length i am talking about is for \alpha=[c] in pi_1(M,p) length(\alpha) is the infimum length of loops that are homotpic to c and not freely homotopic |
Jun
24 |
comment |
riemannian length of an element of the fundamental group of a manifold
is there is some algebraic properties of the fundamental group that can garuentee the property without talking about curvature say for example if the fundamental group is torsion free |
Jun
24 |
comment |
riemannian length of an element of the fundamental group of a manifold
under what conditions the statement is true ? and can the length of \alpha^2 be less the length of \alpha ? |
Jun
24 |
asked | riemannian length of an element of the fundamental group of a manifold |
Jun
18 |
comment |
fundamental groups of surfaces
how do you prove thay every subgroup of infinite index is free ? |
Jun
18 |
asked | fundamental groups of surfaces |
Apr
30 |
awarded | Student |
Apr
30 |
comment |
systole and residualy finite fundamental group
we know that the geometric length is less then c\times( the word length )where (c>0) so every ball of radius R (for the word length) is in some ball of radius cR of the geometric length but we don't know the opposite !!!! |
Apr
30 |
comment |
systole and residualy finite fundamental group
the problem is for any g_i in the fundamental group with length(g)<R we can find a subgroup H_i of finite index that doesn't contain it . so the normal subgroup N will be the instersection of all H_i and here can we guarentee that N is of finite index ?? i know that the intersection of a finite number of subgroups of finite index is of finite index but since we could have an infinite number of g_i of length less then R this would cause a problem |
Apr
29 |
asked | systole and residualy finite fundamental group |
Apr
13 |
answered | Introductory text on geometric group theory? |