### Rigidity of K-Theory under Deformation Quantization, by Jonathan Rosenberg

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.

Jonathan Rosenberg <jmr@math.umd.edu>