In this paper, we study the space of metrics of positive scalar curvature using methods from coarse geometry. Given a closed spin manifold M with fundamental group G, Stephan Stolz introduced the positive scalar curvature exact sequence. Higson and Roe introduced a K-theory exact sequence in K-Theory. The K-theory groups in question are the home of interesting (secondary) invariants, in particular the rho-class of a metric of positive scalar curvature. One of our main results is the construction of a map from the Stolz exact sequence to the Higson–Roe exact sequence (commuting with all arrows), using coarse index theory throughout.
Rho-classes, index theory and Stolz' positive scalar curvature sequence / Piazza, Paolo; T., Schick. - In: JOURNAL OF TOPOLOGY. - ISSN 1753-8416. - STAMPA. - 7:(2014), pp. 965-1004. [10.1112/jtopol/jtt048]
Rho-classes, index theory and Stolz' positive scalar curvature sequence.
PIAZZA, Paolo;
2014
Abstract
In this paper, we study the space of metrics of positive scalar curvature using methods from coarse geometry. Given a closed spin manifold M with fundamental group G, Stephan Stolz introduced the positive scalar curvature exact sequence. Higson and Roe introduced a K-theory exact sequence in K-Theory. The K-theory groups in question are the home of interesting (secondary) invariants, in particular the rho-class of a metric of positive scalar curvature. One of our main results is the construction of a map from the Stolz exact sequence to the Higson–Roe exact sequence (commuting with all arrows), using coarse index theory throughout.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.