5 papers
Biquotient vector bundles with no inverse
Jason DeVito, David González-Álvaro
In previous work, the second author and others have found conditions on a homogeneous space which imply that, up to stabilization, all vector bundles over admit Riemann…
Diffeomorphic souls and disconnected moduli spaces of nonnegatively curved metrics
Igor Belegradek, David González-Álvaro
We give examples of open manifolds that carry infinitely many complete metrics of nonnegative sectional curvature such that they all have the same soul, and their isometry classes…
Moduli space of metrics of nonnegative sectional or positive Ricci curvature on homotopy real projective spaces
Anand Dessai, David González-Álvaro
We show that the moduli space of metrics of nonnegative sectional curvature on every homotopy has infinitely many path components. We also show that in each dim…
The stable converse soul question for positively curved homogeneous spaces
David González-Álvaro, Marcus Zibrowius
The stable converse soul question (SCSQ) asks whether, given a real vector bundle \(E\) over a compact manifold, some stabilization \(E\times\R^k\) admits a metric with non-negativ…
A note on the Petersen-Wilhelm conjecture
David González-Álvaro, Marco Radeschi
In this note we consider submersions from compact manifolds, homotopy equivalent to the Eschenburg or Bazaikin spaces of positive curvature. We show that if the submersion is nontr…