Smoothing 3-dimensional polyhedral spaces
Nina Lebedeva Vladimir Matveev Anton Petrunin Vsevolod Shevchishin
Electronic Research Announcements 2015, 22(0): 12-19 doi: 10.3934/era.2015.22.12
We show that 3-dimensional polyhedral manifolds with nonnegative curvature in the sense of Alexandrov can be approximated by nonnegatively curved 3-dimensional Riemannian manifolds.
keywords: Polyhedral space nonnegative curvature. smoothing
Harmonic functions on Alexandrov spaces and their applications
Anton Petrunin
Electronic Research Announcements 2003, 9(0): 135-141
keywords: XXXX
Curvature bounded below: A definition a la Berg--Nikolaev
Nina Lebedeva Anton Petrunin
Electronic Research Announcements 2010, 17(0): 122-124 doi: 10.3934/era.2010.17.122
We give a new characterization of spaces with nonnegative curvature in the sense of Alexandrov.
keywords: Alexandrov space curvature.
On the torsion in the center conjecture
Vitali Kapovitch Anton Petrunin Wilderich Tuschmann
Electronic Research Announcements 2018, 25(0): 27-35 doi: 10.3934/era.2018.25.004

We present a condition for towers of fiber bundles which implies that the fundamental group of the total space has a nilpotent subgroup of finite index whose torsion is contained in its center. Moreover, the index of the subgroup can be bounded in terms of the fibers of the tower.

Our result is motivated by the conjecture that every almost nonnegatively curved closed $ m $-dimensional manifold $ M $ admits a finite cover $ \tilde M $ for which the number of leafs is bounded in terms of $ m $ such that the torsion of the fundamental group $ π_1 \tilde M $ lies in its center.

keywords: nonnegative curvature nilpotent tower of fiber bundles

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