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 rho-invariant and certain splitting invariants. We survey the classification of fake lens spaces which includes the classification up to homotopy, up to simple homotopy and up to homeomorphism, employing methods of homotopy theory, algebraic K-theory and surgery theory. Finally we discuss the join construction which builds fake lens spaces from other fake lens spaces of a lower dimension.
lens space, fake lens space, Reidemeister torsion, rho-invariant, splitting invariants, surgery, structure set, join construction
Primary: 57R65, 57S25
|Received:||31st March 2012|
|Revised:||4th January 2013, 8th March 2013|
|Accepted:||20th March 2013|
|Published:||25th April 2013|