JournalsjncgVol. 14, No. 2pp. 441–486

Additivity of higher rho invariant for the topological structure group from a differential point of view

  • Baojie Jiang

    Chongqing University, China
  • Hongzhi Liu

    Shanghai University of Finance and Economics, China
Additivity of higher rho invariant for the topological structure group from a differential point of view cover

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Abstract

In [16], Weinberger, Xie, and Yu proved that higher rho invariant associated to homotopy equivalence defines a group homomorphism from the topological structure group to the analytic structure group, KK-theory of certain geometric CC^*-algebras, by piecewise-linear approach. In this paper, we adapt part of Weinberger, Xie, and Yu’s work, to give a differential geometry theoretic proof of the additivity of the map from the topological structure group to KK-theory of certain CC^*-algebra induced by higher rho invariant associated to orientation-preserving homotopy equivalence.

Cite this article

Baojie Jiang, Hongzhi Liu, Additivity of higher rho invariant for the topological structure group from a differential point of view. J. Noncommut. Geom. 14 (2020), no. 2, pp. 441–486

DOI 10.4171/JNCG/369