Title: Porosity and Differentiability of Lipschitz Maps from Stratified Groups to Banach Homogeneous Groups,
Abstract: Let $f$ be a Lipschitz map from a subset $A$ of a stratified group to a
Banach homogeneous group. We show that directional derivatives of $f$ act as
homogeneous homomorphisms at density points of $A$ outside a $\sigma$-porous
set. At density points of $A$ we establish a pointwise characterization of
differentiability in terms of directional derivatives. We use these new results
to obtain an alternate proof of almost everywhere differentiability of
Lipschitz maps from subsets of stratified groups to Banach homogeneous groups
satisfying a suitably weakened Radon-Nikodym property. As a consequence we also
get an alternative proof of Pansu's Theorem.