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The item of this publication is the quantum mechanism that permits the macroscopic quantum coherence of a superconducting condensate to withstand to the assaults of hot temperature. approach to this primary challenge of recent physics is required for the layout of room temperature superconductors, for controlling the decoherence results within the quantum desktops and for the certainty of a potential position of quantum coherence in residing subject that's debated this day in quantum biophysics.

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It follows that the fundamental class of closed locally symmetric spaces is bounded; as explained by M. e. a non-trivial lower bound for its volume with respect to any (suitably normalised) Riemannian metric. 24in Algebraic topology, Aarhus 1978, 109–119, Springer 1979. ´ (56):5–99, 1982. Math. IHES, 26PhD thesis, ETHZ Diss. Nr. 15636, 2004. 27J. , 65(1):19–59, 2003. 28Acta Mathematica, to appear. 29Simplicial volume of locally symmetric spaces covered by SL (R)/SO(3), 3 preprint. 25Publ. GUIDO’S BOOK OF CONJECTURES 39 Many more questions are related to the above conjecture via the following steps listed in increasing order of refinement: (i) find a bounded cocycle representing a given class; (ii) establish a sharp numerical bound for that class; (iii) determine the equivalence class of the cocycle up to boundaries of bounded cochains only.

Renault, Amenable groupoids. Monographs of L’Enseignement Math´ematique, 36. Geneva, 2000. 20N. Higson and J. Roe, Amenable group actions and the Novikov conjecture, J. Reine Angew. Math. 519 (2000), 143–153. 21E. Guentner and J. Kaminker, Exactness and the Novikov conjecture, Topology 41 (2002), no. 2, 411–418. 22N. Ozawa, Amenable actions and exactness for discrete groups, C. R. Acad. Sci. Paris S´er. I Math. 330 (2000), no. 8, 691–695. 23J. Brodzki, G. A. Niblo, N. J. OA/0603621. 36 GUIDO’S BOOK OF CONJECTURES 15.

Whitehead, Math. Proc. Camb. Phil. Soc. 119 (1996), 493–495. : L2 -Invariants: Theory and Applications to Geometry and K-Theory, Ergeb. Math. , 3. Folge, Bd 44, Springer-Verlag, Berlin (2002). (8) Whitehead, J. H. : On adding relations to homotopy groups, Annals of Math. 42 (1941), 409–428. 32 GUIDO’S BOOK OF CONJECTURES 13. Martin R. Bridson and Michael Tweedale Putative relation gaps Dear Guido, We thought that you might enjoy the following concrete speculations concerning the efficiency of finite group-presentations.

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