Volume 5, issue 2 (2001)

Download this article
For printing
Recent Issues

Volume 27
Issue 2, 417–821
Issue 1, 1–415

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
Manifolds with singularities accepting a metric of positive scalar curvature

Boris Botvinnik

Geometry & Topology 5 (2001) 683–718

arXiv: math.DG/9910177


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.

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, $\mathcal{A}(1)$–modules
Mathematical Subject Classification 2000
Primary: 57R15
Secondary: 53C21, 55T15, 57R90
Forward citations
Received: 2 November 1999
Revised: 28 August 2001
Accepted: 26 September 2001
Published: 26 September 2001
Proposed: Ralph Cohen
Seconded: Haynes Miller, Steven Ferry
Boris Botvinnik
Department of Mathematics
University of Oregon
Oregon 97403