Let M0,n+1 be the moduli space of genus zero Riemann surfaces with n+1 marked points. In this paper we compute H∗Σn(M0,n+1;Fp)
Nearby in the stack
and
H∗Σn(M0,n+1;Fp(±1))
for any
n∈N
and any prime
p
, where
Fp(±1)
denotes the sign representation of the symmetric group
Σn
. The interest in these homology groups is twofold: on the one hand classes in these equivariant homology groups parametrize homology operations for gravity algebras. On the other hand the homotopy quotient