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John R. Klein

  1. From Rational Homotopy to K-Theory for Continuous Trace Algebras.

    Втр, 09/22/2009 - 14:09 — SomNambul
    Authors: John R. Klein, Claude L. Schochet, Samuel B. Smith
    Subjects: Operator Algebras
    Abstract

    Let $A$ be a unital $C^*$-algebra. Its unitary group, $UA$, contains a wealth
    of topological information about $A$. However, the homotopy type of $UA$ is out
    of reach even for $A = M_2(\CC)$. There are two simplifications which have been
    considered. The first, well-traveled road, is to pass to $\pi_*(U(A\otimes \KK
    ))$ which is isomorphic (with a degree shift) to $K_*(A)$. This approach has
    led to spectacular success in many arenas, as is well-known.

  2. From Rational Homotopy to K-Theory for Continuous Trace Algebras.

    Втр, 09/22/2009 - 14:09 — SomNambul
    Authors: John R. Klein, Claude L. Schochet, Samuel B. Smith
    Subjects: Operator Algebras
    Abstract

    Let $A$ be a unital $C^*$-algebra. Its unitary group, $UA$, contains a wealth
    of topological information about $A$. However, the homotopy type of $UA$ is out
    of reach even for $A = M_2(\CC)$. There are two simplifications which have been
    considered. The first, well-traveled road, is to pass to $\pi_*(U(A\otimes \KK
    ))$ which is isomorphic (with a degree shift) to $K_*(A)$. This approach has
    led to spectacular success in many arenas, as is well-known.

  3. Continuous trace C*-algebras, gauge groups and rationalization.

    Пт, 08/21/2009 - 19:51 — SomNambul
    Authors: John R. Klein, Claude L. Schochet, Samuel B. Smith
    Subjects: Algebraic Topology
    Abstract

    Let \zeta be an n-dimensional complex matrix bundle over a compact metric
    space X and let A_\zeta denote the C*-algebra of sections of this bundle. We
    determine the rational homotopy type as an H-space of UA_\zeta, the group of
    unitaries of A_\zeta. The answer turns out to be independent of the bundle
    \zeta and depends only upon n and the rational cohomology of X. We prove
    analogous results for the gauge group and the projective gauge group of a
    principal bundle over a compact metric space X.

  4. Continuous trace C*-algebras, gauge groups and rationalization.

    Пт, 08/21/2009 - 19:51 — SomNambul
    Authors: John R. Klein, Claude L. Schochet, Samuel B. Smith
    Subjects: Algebraic Topology
    Abstract

    Let \zeta be an n-dimensional complex matrix bundle over a compact metric
    space X and let A_\zeta denote the C*-algebra of sections of this bundle. We
    determine the rational homotopy type as an H-space of UA_\zeta, the group of
    unitaries of A_\zeta. The answer turns out to be independent of the bundle
    \zeta and depends only upon n and the rational cohomology of X. We prove
    analogous results for the gauge group and the projective gauge group of a
    principal bundle over a compact metric space X.

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