Abstract
Recently, Connes [3] initiated a new index theory for both dynamical systems and foliated manifolds, which is quite useful to cases with pathological ambient spaces for which the Atiyah-Singer index theory is no longer applicable. The main ideas of his theory are based on both K-theory and cyclic cohomology of algebras, whose validity is illustrated in many papers.
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Takai, H. (1991). On The Baum-Connes Conjecture. In: Araki, H., Kadison, R.V. (eds) Mappings of Operator Algebras. Progress in Mathematics, vol 84. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0453-4_7
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DOI: https://doi.org/10.1007/978-1-4612-0453-4_7
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