منابع مشابه
Dirac Operators on 4-manifolds
Dirac operators are important geometric operators on a manifold. The Dirac operator DA on the four dimensional Euclidean space M = R is the order one differential operator whose square DA ◦ DA is the Euclidean Laplacian − ∑4 i=1 ∂ψ ∂xi . However, this is not possible unless we allow coefficients for this linear operator to be matrix-valued. Let M = R be the four dimensional Euclidean space with...
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Consider the class of n-dimensional Riemannian spin manifolds with bounded sectional curvatures and diameter, and almost non-negative scalar curvature. Let r = 1 if n = 2, 3 and r = 2 + 1 if n ≥ 4. We show that if the square of the Dirac operator on such a manifold has r small eigenvalues, then the manifold is diffeomorphic to a nilmanifold and has trivial spin structure. Equivalently, if M is ...
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This paper studies Dirac operators on end-periodic spin manifolds of dimension at least 4. We provide a necessary and sufficient condition for such an operator to be Fredholm for a generic end-periodic metric. We make use of end-periodic Dirac operators to give an analytical interpretation of an invariant of non-orientable smooth 4-manifolds due to Cappell and Shaneson. From this interpretation...
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We give a local normal form for Dirac structures. As a consequence, we show that the dimensions of the pre-symplectic leaves of a Dirac manifold have the same parity. We also show that, given a point m of a Dirac manifold M , there is a well-defined transverse Poisson structure to the pre-symplectic leaf P through m. Finally, we describe the neighborhood of a pre-symplectic leaf in terms of geo...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1990
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-1990-0998124-1