Fake $13$-projective spaces with cohomogeneity one actions

Cohomogeneity One Actions on Noncompact Symmetric Spaces of Rank One

We classify, up to orbit equivalence, all cohomogeneity one actions on the hyperbolic planes over the complex, quaternionic and Cayley numbers, and on the complex hyperbolic spaces CHn, n ≥ 3. For the quaternionic hyperbolic spaces HHn, n ≥ 3, we reduce the classification problem to a problem in quaternionic linear algebra and obtain partial results. For real hyperbolic spaces, this classificat...

Arithmetic Fake Projective Spaces and Arithmetic Fake Grassmannians

Mutations of Fake Weighted Projective Spaces

We characterise mutations between fake weighted projective spaces, and give explicit formulas for how the weights and multiplicity change under mutation. In particular, we prove that multiplicity-preserving mutations between fake weighted projective spaces are mutations over edges of the corresponding simplices. As an application, we analyse the canonical and terminal fake weighted projective s...

Cohomogeneity One Actions on Some Noncompact Symmetric Spaces of Rank Two

We classify, up to orbit equivalence, the cohomogeneity one actions on the noncompact Riemannian symmetric spaces G2 /G2, SL3(C)/SU3 and SO 2,n+2/SO2SOn+2, n ≥ 1.

All Finite Groups Act on Fake Complex Projective Spaces

We prove the result asserted in the title. The object of this note is to prove the assertion of its title in a slightly more precise form that shows that one can somewhat control the normal representation at a fixed point and that there is an infinite amount of choice for the rational Pontrjagin classes. This result is in sharp contrast to a conjecture of Ted Pétrie [5] that only homotopy CP"'s...