By Daniel Iagolnitzer

Over one thousand mathematicians participated within the Paris foreign convention on Mathematical Physics and its satellite tv for pc convention on topology, strings and integrable types. This quantity comprises the various highlights, together with subject matters akin to conformable box concept and normal relativity.

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More specifically J is here the boundary of the set B = {z G C; sup \

E. harmonic forms, and the image of d + d*. Thus any u e H q , orthogonal to harmonic forms, can be written as u = da, a G L 2 (V, Aj^"1! 1*), using the formula d* = - * d* for the adjoint of d. Moreover the equality cj = -Mp da determines da uniquely since Il H 2 d a ll2 = Il á a ll2 G Aq "1 T*). f,F , 7 ) over C 00 (V'). We let H = 7-fo 0 H n(V, C) be the direct sum of Ho with the finite dimensional Hilbert space of harmonic n-forms on V, which we identify with the n dimensional cohomology group H n(V, C).

It is interesting in that respect to relate the Polyakov action dis cussed below with the p-adic string action discussed in []. The latter is obtained using the usual trace instead of the Dixmier trace, due to the O-dimensionality of the p-adic situation. 1 P ertu rb atio n of Fredholm m odules by th e com m utant von N eum ann algebra Let M be a von Neumann algebra and M2 (M) = M2 (C) O M. 8) Quantized Calculus and Applications 25 P roposition 4. a) G is a subgroup o /G I^ M ), and is isomorphic to Glq(M ) b) Let p, = p* € M, ||/x|| < i.