Positive Scalar Curvature due to the Cokernel of the Classifying Map

Symmetry Integrability and Geometry-Methods and Applications

article

Thomas Schick¹  Vito Felice Zenobi² 

[1] Mathematisches Institut;Dipartimento di Matematica, Sapienza Università di Roma

关键词: positive scalar curvature;    bordism;    concordance;    Stolz exact sequence;    analytic surgery exact sequence;    secondary index theory;    higher index theory;    K-theory;   

DOI  :  10.3842/SIGMA.2020.129

来源: National Academy of Science of Ukraine

【 摘 要 】

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 $\pi_1(M)$.

【 授权许可】

Unknown