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.
2014
Dirac operators; surgery sequences; metrics of positive scalar curvature
01 Pubblicazione su rivista::01a Articolo in rivista
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/780582
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