Fake lens spaces *

of the Manifold Atlas ( 2013 ) Fake lens spaces *

A fake lens space is an orbit space of a free action of a finite cyclic group on a sphere and as such it is a generalization of a classical lens space. The invariants of fake lens spaces described here are their homotopy groups, homology groups, a certain k-invariant, the Reidemeister torsion, the ρ-invariant and certain splitting invariants. We survey the classification of fake lens spaces whi...

On the Classification of Fake Lens Spaces

In the first part of the paper we present a classification of fake lens spaces of dimension ≥ 5 whose fundamental group is the cyclic group of order any N ≥ 2. The classification is stated in terms of the simple structure sets in the sense of surgery theory. The results use and extend the results of Wall and others in the cases N = 2 and N odd and the results of the authors of the present paper...

On Fake Lens Spaces with the Fundamental Group of Order a Power of 2

We present a classification of fake lens spaces of dimension ≥ 5 which have as fundamental group the cyclic group of order N = 2K , in that we extend the results of Wall and others in the case N = 2. Introduction A fake lens space is the orbit space of a free action of a finite cyclic group G on a sphere S2d−1. It is a generalization of the notion of a lens space which is the orbit space of a f...

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...

Arithmetic Fake Projective Spaces and Arithmetic Fake Grassmannians