Abstract:
In this paper the homological K-functor is defined on the category of involutory Banach algebras, and Bott periodicity is proved, along with a series of theorems corresponding to the Eilenberg–Steenrod axioms. As an application, a generalization of the Atiyah–Singer index theorem is obtained, and some problems connected with representation rings of discrete groups and higher signatures of smooth manifolds are discussed.
Bibliography: 16 items.
This publication is cited in the following 57 articles:
Baiying Ren, Hang Wang, Zijing Wang, “An equivariant index theorem on ℝn in the context of continuous fields of C*-algebras”, Sci. China Math., 2025
Kengo Matsumoto, Mathematical Physics Studies, Symbolic Dynamical Systems and C*-Algebras, 2025, 143
Xiaoman Chen, Kun Gao, Jiawen Zhang, “The strongly quasi-local coarse Novikov conjecture and Banach spaces with Property (H)”, Kyoto J. Math., 64:1 (2024)
Kengo Matsumoto, “K-theoretic duality for extensions of Cuntz–Krieger algebras”, Journal of Mathematical Analysis and Applications, 531:2 (2024), 127827
Hang Wang, Chaohua Zhang, Dapeng Zhou, “Localization C∗−algebras and index pairing”, J. Homotopy Relat. Struct., 18:1 (2023), 1
Zheng Luo, Qin Wang, Yazhou Zhang, “The coarse Novikov conjecture for coarse fibrations over Banach spaces with Property (H)”, Ann. Funct. Anal., 13:3 (2022)
Jens Kaad, “On the Unbounded Picture of KK-Theory”, SIGMA, 16 (2020), 082, 21 pp.
Rufus Willett, Guoliang Yu, Higher Index Theory, 2020
Chi-Kwong Fok, “Equivariant twisted Real K-theory of compact Lie groups”, Journal of Geometry and Physics, 124 (2018), 325
Jonathan Rosenberg, Open Problems in Mathematics, 2016, 377
Emil Prodan, Hermann Schulz-Baldes, “Generalized Connes–Chern characters inKK-theory with an application to weak invariants of topological insulators”, Rev. Math. Phys., 28:10 (2016), 1650024
Xiaoman Chen, Qin Wang, Guoliang Yu, “The coarse Novikov conjecture and Banach spaces with Property (H)”, Journal of Functional Analysis, 2015
Fabio Cipriani, Daniele Guido, Tommaso Isola, Jean-Luc Sauvageot, “Spectral triples for the Sierpinski gasket”, Journal of Functional Analysis, 2014
Xiaoman Chen, Qin Wang, Zhijie Wang, “Fibred coarse embedding into non-positively curved manifolds and higher index problem”, Journal of Functional Analysis, 2014
R.J.. Deeley, “Geometric K-homology with coefficients II: The Analytic Theory and Isomorphism”, J. K-Theory, 2013, 1
Xiaoman Chen, Qin Wang, Guoliang Yu, “The maximal coarse Baum–Connes conjecture for spaces which admit a fibred coarse embedding into Hilbert space”, Advances in Mathematics, 249 (2013), 88
Moulay-Tahar Benameur, Alan L. Carey, “Higher spectral flow and an entire bivariant JLO cocycle”, J K-Theor, 11:1 (2013), 183
Rufus Willett, Guoliang Yu, “Higher index theory for certain expanders and Gromov monster groups, I”, Advances in Mathematics, 229:3 (2012), 1380
Roger Howe, Mathematical Methods in Systems, Optimization, and Control, 2012, 221
Ulrich Bunke, Thomas Schick, Springer Proceedings in Mathematics, 17, Global Differential Geometry, 2012, 303
Citation in format AMSBIB
Contact us: