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comment 
Growth of the number of generators in hyperbolic groups
The existence of hyperbolic HNN extensions (eg some freebycyclic groups) makes this tricky. Does it help to assume that the hyperbolic group has trivial abelianization? 
Dec 21 
awarded  Necromancer 
Dec 21 
comment 
Do geodesics in SL2R map to geodesics in the hyperbolic plane?
Can ballistic curves be reparameterized to become geodesics? (Perhaps allowing variable speed?) 
Dec 21 
comment 
Do geodesics in SL2R map to geodesics in the hyperbolic plane?
Geodesics that point in the direction of the SO(2) subgroup cannot map to geodesics. I believe that these map to the constant path. If so, do you allow the constant path as a geodesic? 
Dec 21 
revised 
Quotient of the hyperbolic plane with respect to commutator group of $\pi_1(\Sigma_g)$
translated from notation of OP 
Dec 21 
revised 
Quotient of the hyperbolic plane with respect to commutator group of $\pi_1(\Sigma_g)$
fixed typo and wording 
Dec 21 
awarded  Revival 
Dec 21 
revised 
Quotient of the hyperbolic plane with respect to commutator group of $\pi_1(\Sigma_g)$
edited tags. 
Dec 21 
answered  Quotient of the hyperbolic plane with respect to commutator group of $\pi_1(\Sigma_g)$ 
Dec 18 
reviewed  Approve Rooks in three dimensions 
Dec 13 
answered  Dilatation of surface diffeomorphisms 
Dec 6 
reviewed  Approve Question regarding Laplace equation under Evans setting 
Nov 24 
comment 
Additivity of simplicial volume
Thilo Kuessner's thesis should have a selfcontained account. However, it does not appear to be easily available online. Perhaps contact him directly. 
Nov 24 
comment 
Additivity of simplicial volume
A small error in what you write  a torus cannot appear in the geodesic boundary of a hyperbolic manifold. Perhaps you mean cusp. 
Nov 23 
revised 
Realizing proper pure octonions as conjugates
Removed reference to "dance of seven veils". 
Nov 10 
awarded  Yearling 
Nov 9 
comment 
Fantastic properties of Z/2Z
Oh, that looks nice  I'll have to think about that. By the way, I sort of want to edit your answer: $Z_2 * Z_2$ is the only nontrivial free product that is twoended (thus is virtually cyclic) while all others have infinitely many ends (so contain rank two free groups, etc). 
Nov 9 
comment 
Fantastic properties of Z/2Z
There are several nice identities  the simplest after a few moments thought is $[x^2, y^2]$. 
Nov 9 
reviewed  Approve Exploiting the Linearity of the Pullback 
Nov 7 
answered  Unseparability of two linked rings in higher dimensions 