A counterexample to a conjecture about positive scalar curvature
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- by Daniel Pape and Thomas Schick PDF
- Proc. Amer. Math. Soc. 143 (2015), 3165-3168 Request permission
Abstract:
In his article in Proc. Amer. Math. Soc. 138 (2010), no. 5, 1621–1632, S. Chang conjectures that a closed smooth manifold $M$ with non-spin universal covering admits a metric of positive scalar curvature if and only if a certain homological condition is satisfied. We present a counterexample to this conjecture, based on the counterexample to the unstable Gromov-Lawson-Rosenberg conjecture given in the second author’s article in Topology 37 (1998), no. 6, 1165–1168.References
- Stanley Chang, Positive scalar curvature of totally nonspin manifolds, Proc. Amer. Math. Soc. 138 (2010), no. 5, 1621–1632. MR 2587446, DOI 10.1090/S0002-9939-09-09483-0
- William Dwyer, Thomas Schick, and Stephan Stolz, Remarks on a conjecture of Gromov and Lawson, High-dimensional manifold topology, World Sci. Publ., River Edge, NJ, 2003, pp. 159–176. MR 2048721, DOI 10.1142/9789812704443_{0}008
- Michael Joachim and Thomas Schick, Positive and negative results concerning the Gromov-Lawson-Rosenberg conjecture, Geometry and topology: Aarhus (1998), Contemp. Math., vol. 258, Amer. Math. Soc., Providence, RI, 2000, pp. 213–226. MR 1778107, DOI 10.1090/conm/258/04066
- Daniel Pape, Index theory and positive scalar curvature, Ph.D. thesis, Georg-August-Universität of Göttingen, 2011.
- Thomas Schick, A counterexample to the (unstable) Gromov-Lawson-Rosenberg conjecture, Topology 37 (1998), no. 6, 1165–1168. MR 1632971, DOI 10.1016/S0040-9383(97)00082-7
Additional Information
- Daniel Pape
- Affiliation: Georg-August-Universität Göttingen, Bunsenstraße 3, 37073 Göttingen, Germany
- Email: pape@uni-math.gwdg.de
- Thomas Schick
- Affiliation: Georg-August-Universität Göttingen, Bunsenstraße 3, 37073 Göttingen, Germany
- MR Author ID: 635784
- Email: schick@uni-math.gwdg.de
- Received by editor(s): August 9, 2013
- Received by editor(s) in revised form: June 14, 2013
- Published electronically: March 18, 2015
- Additional Notes: The first author was supported by the German Research Foundation (DFG) through the Research Training Group 1493 “Mathematical structures in modern quantum physics”
The second author was partially funded by the Courant Research Center “Higher order structures in Mathematics” within the German initiative of excellence - Communicated by: Daniel Ruberman
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 3165-3168
- MSC (2010): Primary 57R65
- DOI: https://doi.org/10.1090/S0002-9939-2015-12330-1
- MathSciNet review: 3336640