Boris Botvinnik
University of Oregon
59 Papers
337 Citations
Boris Botvinnik is an academic researcher from University of Oregon. The author has contributed to research in topics: Scalar curvature & Manifold. The author has an hindex of 15, co-authored 58 publications. Previous affiliations of Boris Botvinnik include Portland State University.
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Papers
The Gromov-Lawson-Rosenberg conjecture for groups with periodic cohomology
Abstract: vanishes Note that index D M unlike the dimension of the ker nel and the dimension of the cokernel of D M is independent of the metric used in the construction of D M In fact according to the Atiyah Singer Index Theorem it is equal to a topological invariant A M the A genus ofM cf Ch III Thm We recall that A M is a characteristic number de ned by evaluating a certain polyno mial in the Pontrjagin classes of the tangent bundle on the fundamental class of M Lichnerowicz result was generalized by Hitchin who constructs a version of the Dirac operator D M which is selfadjoint and commutes with an action of the Cli ord algebra C n where n is the dimension of
Infinite loop spaces and positive scalar curvature
TL;DR: In this paper, the authors studied the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds and proved the existence of a similar factorisation for manifolds of odd dimension $2n+1 \geq 7.
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Infinite loop spaces and positive scalar curvature
TL;DR: In this paper, the authors studied the homotopy type of the space of metrics of positive scalar curvature on high-dimensional compact spin manifolds and showed that the natural KO-orientation from the infinite loop space of the Madsen-Tillmann-Weiss spectrum factors (up to homoopy) through the space for metric metrics on any 2n-dimensional spin manifold.
The relative Yamabe invariant
Kazuo Akutagawa,Boris Botvinnik +1 more
TL;DR: In this paper, the authors define a relative Yamabe invariant of a smooth manifold with given conformal class on its boundary, and develop an approximation technique which leads to gluing theorems of two manifolds along their boundaries.
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The Yamabe invariants of orbifolds and cylindrical manifolds, and $L^2$-harmonic spinors
Kazuo Akutagawa,Boris Botvinnik +1 more
TL;DR: In this article, the Yamabe invariants of cylindrical manifolds and compact orbifolds with a finite number of singularities were studied by means of conformal geometry and the Atiyah-Patodi-Singer $L^2$-index theory.
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