Geometry & Topology, Vol. 5 (2001)
Paper no. 22, pages 683--718.
Manifolds with singularities accepting a metric of positive scalar curvature
Boris Botvinnik
Abstract.
We study the question of existence of a Riemannian metric of positive
scalar curvature metric on manifolds with the Sullivan-Baas
singularities. The manifolds we consider are Spin and simply
connected. We prove an analogue of the Gromov-Lawson Conjecture for
such manifolds in the case of particular type of singularities. We
give an affirmative answer when such manifolds with singularities
accept a metric of positive scalar curvature in terms of the index of
the Dirac operator valued in the corresponding "K-theories with
singularities". The key ideas are based on the construction due to
Stolz, some stable homotopy theory, and the index theory for the Dirac
operator applied to the manifolds with singularities. As a
side-product we compute homotopy types of the corresponding
classifying spectra.
Keywords.
Positive scalar curvature, Spin manifolds, manifolds with
singularities, Spin cobordism, characteristic classes in K-theory,
cobordism with singularities, Dirac operator, K-theory with
singularities, Adams spectral sequence, A(1)-modules.
AMS subject classification.
Primary: 57R15.
Secondary: 53C21, 55T15, 57R90.
DOI: 10.2140/gt.2001.5.683
E-print: arXiv:math.DG/9910177
Submitted to GT on 2 November 1999.
(Revised 28 August 2001.)
Paper accepted 26 September 2001.
Paper published 26 September 2001.
Notes on file formats
Boris Botvinnik
Department of Mathematics, University of Oregon
Eugene, OR 97403, USA
Email: botvinn@math.uoregon.edu
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