Journal of Differential Geometry

Index Theory with Bounded Geometry, the Uniformly Finite  Class, and Infinite Connected Sums

Kevin Whyte

Full-text: Open access

Abstract

We prove a vanishing theorem in uniformly finite homology for the  genus of a complete spin manifold of bounded geometry and non-negative scalar curvature. This theorem is then applied to obstruct the existence of such metrics for some infinite connected sums, giving a converse to a theorem of Block and Weinberger.

Article information

Source
J. Differential Geom., Volume 59, Number 1 (2001), 1-14.

Dates
First available in Project Euclid: 20 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1090349278

Digital Object Identifier
doi:10.4310/jdg/1090349278

Mathematical Reviews number (MathSciNet)
MR1909246

Zentralblatt MATH identifier
1031.58013

Citation

Whyte, Kevin. Index Theory with Bounded Geometry, the Uniformly Finite  Class, and Infinite Connected Sums. J. Differential Geom. 59 (2001), no. 1, 1--14. doi:10.4310/jdg/1090349278. https://projecteuclid.org/euclid.jdg/1090349278


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