Mishchenko-Fomenko index theorem in nLab
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Context
Index theory
noncommutative topology, noncommutative geometry
noncommutative stable homotopy theory
genus, orientation in generalized cohomology
Definitions
Index theorems
Higher genera
Functional analysis
Overview diagrams
Basic concepts
Theorems
Topics in Functional Analysis
Operator algebra
algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
Concepts
quantum mechanical system, quantum probability
interacting field quantization
Theorems
States and observables
Operator algebra
Local QFT
Perturbative QFT
Contents
Idea
The Mishchenko-Fomenko index theorem is a generalization of the Atiyah-Singer index theorem to differential operators on Hilbert module-bundles over some C*-algebra.
References
The original English version of the original work is
- A.S. Mishchenko, A.T. Fomenko, The index of elliptic operators over C-algebras., Math. USSR, Izv. 15 (1980), 87–112.
A more explicit rederivation is in section 6.1 of
- Thomas Schick, -index, KK-theory, and connections, New York J. Math. 11 (2005) (arXiv:math/0306171)
Last revised on May 20, 2013 at 12:46:49. See the history of this page for a list of all contributions to it.