13 citations · 59 across the 34 of their papers we have counts for
44 papers
Point selections from Jordan domains in Riemannian Surfaces
Igor Belegradek, Mohammad Ghomi
Using fiber bundle theory and conformal mappings, we continuously select a point from the interior of Jordan domains in Riemannian surfaces. This selection can be made equivariant…
Four manifolds with no smooth spines
Igor Belegradek, Beibei Liu
Let be a compact smooth -manifold that deformation retract to a PL embedded closed surface. One can arrange the embedding to have at most one non-locally-flat point, and nea…
Hyperbolization and regular neighborhoods
Igor Belegradek
We show that the hyperbolization of polyhedra pulls back regular neighborhoods of PL submanifolds. Applying this to the Riemannian version of the hyperbolization due to Ontaneda gi…
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…
Iterated circle bundles and infranilmanifolds
Igor Belegradek
We give short proofs of the following two facts: Iterated principal circle bundles are precisely the nilmanifolds. Every iterated circle bundle is almost flat, and hence diffeomorp…
Index theory and deformations of open nonnegatively curved manifolds
Igor Belegradek
We use an index-theoretic technique of Hitchin to show that the space of complete Riemannian metrics of nonnegative sectional curvature on certain open spin manifolds has nontrivia…