Alberto S. Cattaneo

  1. Remarks on Chern-Simons invariants.

    Authors: Alberto S. Cattaneo, Pavel Mnev
    Subjects: Quantum Algebra
    Abstract

    The perturbative Chern-Simons theory is studied in a finite-dimensional
    version or assuming that the propagator satisfies certain properties (as is the
    case, e.g., with the propagator defined by Axelrod and Singer). It turns out
    that the effective BV action is a function on cohomology (with shifted degrees)
    that solves the quantum master equation and is defined modulo certain canonical
    transformations that can be characterized completely. Out of it one obtains
    invariants.

  2. Symplectic Microgeometry I: Micromorphisms.

    Authors: Alberto S. Cattaneo, Benoit Dherin, Alan Weinstein
    Subjects: Symplectic Geometry
    Abstract

    We introduce the notion of symplectic microfolds and symplectic
    micromorphisms between them. They form a monoidal category, which is a version
    of the "category" of symplectic manifolds and canonical relations obtained by
    localizing them around lagrangian submanifolds in the spirit of Milnor's
    microbundles.

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