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seen Sep 27 '11 at 11:16

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?