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2001 Manifolds with singularities accepting a metric of positive scalar curvature
Boris Botvinnik
Geom. Topol. 5(2): 683-718 (2001). DOI: 10.2140/gt.2001.5.683


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.


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Boris Botvinnik. "Manifolds with singularities accepting a metric of positive scalar curvature." Geom. Topol. 5 (2) 683 - 718, 2001.


Received: 2 November 1999; Revised: 28 August 2001; Accepted: 26 September 2001; Published: 2001
First available in Project Euclid: 21 December 2017

zbMATH: 1002.57055
MathSciNet: MR1857524
Digital Object Identifier: 10.2140/gt.2001.5.683

Primary: 57R15
Secondary: 53C21 , 55T15 , 57R90

Keywords: $\mathcal{A}(1)$–modules , $K$–theory with singularities , Adams spectral sequence , characteristic classes in $K$–theory , cobordism with singularities , Dirac operator , manifolds with singularities , positive scalar curvature , Spin cobordism , Spin manifolds

Rights: Copyright © 2001 Mathematical Sciences Publishers


Vol.5 • No. 2 • 2001
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