Mapping Surgery to Analysis I: Analytic Signatures

89 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

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 ”
Mapping Surgery to Analysis III: Exact Sequences (2004, methodology): “In the first paper [ 5 ], we have shown how to associate a homotopy invariant -algebraic signature to suitable chain complexes of Hilbert modules satisfying Poincar´ e duality.”
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 II: Geometric Signatures (2004, methodology): “In the first paper [ 8 ], we defined an analytic signature invariant in -algebra -theory.”