of the Manifold Atlas ( 2013 ) Fake lens spaces *
نویسنده
چکیده
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 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.
منابع مشابه
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...
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