2 citations · 2 across the 3 of their papers we have counts for
7 papers
Singular Riemannian flows and characteristic numbers
Igor Prokhorenkov, Ken Richardson
Let be an even-dimensional, oriented closed manifold. We show that the restriction of a singular Riemannian flow on to a small tubular neighborhood of each connected compon…
Perturbations of basic Dirac operators on Riemannian foliations
Igor Prokhorenkov, Ken Richardson
Using the method of Witten deformation, we express the basic index of a transversal Dirac operator over a Riemannian foliation as the sum of integers associated to the critical lea…
Natural Equivariant Dirac Operators
Igor Prokhorenkov, Ken Richardson
We introduce a new class of natural, explicitly defined, transversally elliptic differential operators over manifolds with compact group actions. Under certain assumptions, the sym…
Semiclassical Asymptotics on Manifolds with Boundary
Nilufer Koldan, Igor Prokhorenkov, Mikhail Shubin
We discuss semiclassical asymptotics for the eigenvalues of the Witten Laplacian for compact manifolds with boundary in the presence of a general Riemannian metric. To this end, we…
Witten deformation and the equivariant index
Igor Prokhorenkov, Ken Richardson
Let be a compact Riemannian manifold endowed with an isometric action of a compact Lie group. The method of the Witten deformation is used to compute the virtual representation…
Perturbations of Dirac operators
Igor Prokhorenkov, Ken Richardson
We study general conditions under which the computations of the index of a perturbed Dirac operator localize to the singular set of the bundle endomorphism in the…