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Vol.37 (1) 2015 — 2 results found.

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Counting Toric Actions on Symplectic Four-Manifolds
C. R. Math. Rep. Acad. Sci. Canada Vol. 37 (1) 2015, pp. 33-40
Y. Karshon; L. Kessler; M. Pinsonnault (Received: 2014/09/15, Revised: 2014/10/07)

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Given a symplectic manifold, we ask in how many different ways can a torus act on it. Classification theorems in equivariant symplectic geometry can sometimes tell that two Hamiltonian torus actions are inequivalent, but often they do not tell whether the underlying symplectic manifolds are (non-equivariantly) symplectomorphic. For two dimensional torus actions on closed symplectic four-manifolds, we reduce the counting question to combinatorics, by expressing the manifold as a symplectic blowup in a way that is compatible with all the torus actions simultaneously.

Nous nous intéressons aux différentes actions d’un tore sur une variété symplectique donnée. En géométrie symplectique équivariante, les théorèmes de classification permettent parfois de distinguer des actions hamiltoniennes de tores géométriquement inéquivalentes. Par contre, ces théorèmes ne permettent habituellement pas de déterminer si les variétés symplectiques sous-jaçentes sont symplectomorphes. Dans le cas des variétés symplectiques de dimension \(4\), nous réduisons le problème d’énumération des actions toriques inéquivalentes à un problème combinatoire en exprimant la variété considérée comme un éclatement symplectique qui est compatible simultanément avec toutes les actions toriques. Ce résultat est obtenu en employant des techniques pseudo-holomorphes.

A Classification of Tracially Approximate Splitting Interval Algebras. II. Existence Theorem
C. R. Math. Rep. Acad. Sci. Canada Vol. 37 (1) 2015, pp. 1–32
Zhuang Niu (Received: 2012/01/26, Revised: 2013/03/26)

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Motivated by Huaxin Lin’s axiomatization of AH-algebras, the class of TASI-algebras is introduced as the class of unital C*-algebras which can be tracially approximated by splitting interval algebras—certain sub-C*-algebras of interval algebras. It is shown that the class of simple separable nuclear TASI-algebras satisfying the UCT is classified by the Elliott invariant. As a consequence, any such TASI-algebra is then isomorphic to an inductive limit of splitting interval algebras together with certain homogeneous C*-algebras—so it is an ASH-algebra.

Une classe de C*-algèbres qui généralisent la classe bien connue TAI de Lin est considérée—basées sur, au lieu de l’intervalle, ce qui pourrait s’appeler l’intervalle fendu ("splitting interval"), de sorte que l’on les appelle la classe TASI. On montre que la classe de C*-algèbres TASI qui sont simples, nucléaires, et à élément unité, qui vérifient le théorème à coefficients universels (UCT), peuvent se classifier d’après l’invariant d’Elliott.

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Most used Keywords

algebraic number theory approximation property automorphisms Bessel functions Boson-fermion correspondence C*-algebra Carmichael number center problem Chebyshev transform classification Classification of simple C*-algebras composition operators continued fractions Cuntz Semigroup elliptic curves fixed point Fourier transform function fields. functoriality general relativity generic property ideals indefinite inner product inductive limits of sub-homogeneous C*- algebras Irrational rotation algebra J-Hermitian matrix K-theory Kahler manifolds L-functions maximal ideal space nonexpansive mapping numerical range orthogonal polynomials Predual space prime number property SP Renormalization rotation algebras Salem number semi-reciprocal polynomials tracially approximate splitting interval algebras unbounded traces uniqueness Weak Markov set Whitney problems

Most used AMS

05C05 11A07 11A55 11B37 11B68 11D09 11D25 11D41 11E04 11F11 11F66 11F67 11G05 11R09 11R11 13B25 14J26 14M25 14P10 17B37 17B67 19K14 19K56 26A51 30C15 30H05 35B 37E10 37E20 37F25 39B72 42C05 43A07 46B20 46L05 46L35 46L40 46L55 46L80 47H10 53B25 53C55 54C60 60F10 83C05

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