dorsal/arxiv
View SchemaRigidity of K-theory under deformation quantization
| Authors | Jonathan Rosenberg |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9607021 |
| URL | https://arxiv.org/abs/q-alg/9607021 |
| Journal | Operator algebras and quantum field theory (Rome, 1996), Internat. Press, 1997, pp. 404-415 |
Abstract
Quantization, at least in some formulations, involves replacing some algebra of observables by a (more non-commutative) deformed algebra. In view of the fundamental role played by K-theory in non-commutative geometry and topology, it is of interest to ask to what extent K-theory remains "rigid" under this process. We show that some positive results can be obtained using ideas of Gabber, Gillet-Thomason, and Suslin. From this we derive that the algebraic K-theory with finite coefficients of a deformation quantization of the functions on a compact symplectic manifold, forgetting the topology, recovers the topological K-theory of the manifold.
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"abstract": "Quantization, at least in some formulations, involves replacing some algebra\nof observables by a (more non-commutative) deformed algebra. In view of the\nfundamental role played by K-theory in non-commutative geometry and topology,\nit is of interest to ask to what extent K-theory remains \"rigid\" under this\nprocess. We show that some positive results can be obtained using ideas of\nGabber, Gillet-Thomason, and Suslin. From this we derive that the algebraic\nK-theory with finite coefficients of a deformation quantization of the\nfunctions on a compact symplectic manifold, forgetting the topology, recovers\nthe topological K-theory of the manifold.",
"arxiv_id": "q-alg/9607021",
"authors": [
"Jonathan Rosenberg"
],
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"q-alg",
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"journal_ref": "Operator algebras and quantum field theory (Rome, 1996), Internat.\n Press, 1997, pp. 404-415",
"title": "Rigidity of K-theory under deformation quantization",
"url": "https://arxiv.org/abs/q-alg/9607021"
},
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