Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

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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