Can I read Collapsing manifolds obtained by Kummer-type constructions on EtoBox?

Collapsing manifolds obtained by Kummer-type constructions by Paternain, Gabriel P.; Petean, Jimmy is a scholarly article available to read on EtoBox.

What is Collapsing manifolds obtained by Kummer-type constructions about?

We construct F-structures on a Bott manifold and on some other manifolds obtained by Kummer-type constructions. We also prove that if M=E#X, where E is a fiber bundle with structure group G and a fiber admitting a G-invariant metric of non-negative sectional curvature and X admits an F-structure with one trivial covering, then one can construct on M a sequence of metrics with sectional curvature uniformly bounded from below and volume tending to zero (i.e. $Vol_K$ (M)=0). As a corollary we prove that all the elements in the Spin cobordism group can be represented by manifolds M with $Vol_K$ (M)==0.

Author

Paternain, Gabriel P.; Petean, Jimmy

Published

2005

Language

EN