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SIGMA 16 (2020), 129, 12 pages arXiv:2006.15965
https://doi.org/10.3842/SIGMA.2020.129
Contribution to the Special Issue on Scalar and Ricci Curvature in honor of Misha Gromov on his 75th Birthday
Positive Scalar Curvature due to the Cokernel of the Classifying Map
Thomas Schick a and Vito Felice Zenobi b
a) Mathematisches Institut, Universität Göttingen, Germany
b) Dipartimento di Matematica, Sapienza Università di Roma, Piazzale Aldo Moro 5 - 00185 - Roma, Italy
Received July 13, 2020, in final form December 04, 2020; Published online December 09, 2020
Abstract
This paper contributes to the classification of positive scalar curvature metrics up to bordism and up to concordance. Let $M$ be a closed spin manifold of dimension $\ge 5$ which admits a metric with positive scalar curvature. We give lower bounds on the rank of the group of psc metrics over $M$ up to bordism in terms of the corank of the canonical map $KO_*(M)\to KO_*(B\pi_1(M))$, provided the rational analytic Novikov conjecture is true for $\pi_1(M)$.
Key words: positive scalar curvature; bordism; concordance; Stolz exact sequence; analytic surgery exact sequence; secondary index theory; higher index theory; K-theory.
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