Mapping Surgery to Analysis II: Geometric Signatures

By N. Higson, J. Roe. 2004

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View Paper: https://www.semanticscholar.org/paper/f7e7deb5c226116fd2aba46d74f573ca5b8f9be4

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In Mathematical Physics

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Positive scalar curvature, higher rho invariants and localization algebras (2013, background): “ee Section 5 below for the precise deﬁnitions). This is analogous to the surgery exact sequence in topology. In fact, for the surgery exact sequence, Higson and Roe constructed a natural homomorphism [15, 16, 17] from the surgery exact sequence to the following exact sequence of K-theory of C∗-algeb”
Mapping Surgery to Analysis I: Analytic Signatures (2004, background): “For more details see the second paper in this series [ 4 ].”
Mapping Surgery to Analysis III: Exact Sequences (2004, background): “In paper II [ 6 ] we have also clarified the relationship between the analytic signature, defined by the procedure of paper I for suitable Poincar´ e complexes, and the analytic index of the signature operator, defined only for manifolds.”
Rho‐classes, index theory and Stolz’ positive scalar curvature sequence (2012, methodology): “ary index theorem 1.22 has been carried out (as indicated in Remark 1.29), also Theorem 1.41 extends to the arbitrary dimensions. 12 PAOLO PIAZZA AND THOMAS SCHICK Remark1.45. In their seminal papers [11, 12, 13] Higson and Roe carry out a a program similar to the one developed here: they construct ”
K-Homology, Assembly and Rigidity Theorems for Relative Eta Invariants (2010, methodology): “In an earlier sequence of papers [22, 23 , 24] we introduced and analyzed “analytic structure groups” S ( ) that measure the failure of the assembly map to be an isomorphism.”