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Random projections of smooth manifolds
 Foundations of Computational Mathematics
, 2006
"... We propose a new approach for nonadaptive dimensionality reduction of manifoldmodeled data, demonstrating that a small number of random linear projections can preserve key information about a manifoldmodeled signal. We center our analysis on the effect of a random linear projection operator Φ: R N ..."
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Cited by 144 (25 self)
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We propose a new approach for nonadaptive dimensionality reduction of manifoldmodeled data, demonstrating that a small number of random linear projections can preserve key information about a manifoldmodeled signal. We center our analysis on the effect of a random linear projection operator Φ: R
TRACE HOMOMORPHISM FOR SMOOTH MANIFOLDS
, 2005
"... Abstract. Let M be a closed connected smooth manifold and G = Diff0(M) denote the connected component of the diffeomorphism group of M containing the identity. The natural action of G on M induces the trace homomorphism on homology. We show that the image of trace homomorphism is annihilated by the ..."
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Abstract. Let M be a closed connected smooth manifold and G = Diff0(M) denote the connected component of the diffeomorphism group of M containing the identity. The natural action of G on M induces the trace homomorphism on homology. We show that the image of trace homomorphism is annihilated
Homotopically equivalent smooth manifolds
 I, Izv. Akad. Nauk SSSR Ser. Mat
, 1964
"... In this paper we introduce a method for the investigation of smooth simply connected manifolds of dimension n ≥ 5 that permits a classification of them with exactness up to orientationpreserving diffeomorphisms. This method involves a detailed investigation of the properties of the socalled Thom c ..."
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Cited by 16 (3 self)
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In this paper we introduce a method for the investigation of smooth simply connected manifolds of dimension n ≥ 5 that permits a classification of them with exactness up to orientationpreserving diffeomorphisms. This method involves a detailed investigation of the properties of the socalled Thom
Derived Smooth Manifolds
"... ... and it is closed under taking arbitrary intersections in a manifold. A derived manifold is a space together with a sheaf of local C∞rings that is obtained by patching together homotopy zerosets of smooth functions on Euclidean spaces. We show that derived manifolds come equipped with a stable ..."
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Cited by 11 (1 self)
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... and it is closed under taking arbitrary intersections in a manifold. A derived manifold is a space together with a sheaf of local C∞rings that is obtained by patching together homotopy zerosets of smooth functions on Euclidean spaces. We show that derived manifolds come equipped with a stable
Deformations of gerbes on smooth manifolds
, 2007
"... Abstract. We identify the 2groupoid of deformations of a gerbe on a C ∞ manifold with the Deligne 2groupoid of a corresponding twist of the DGLA of local Hochschild cochains on C ∞ functions. ..."
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Cited by 7 (6 self)
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Abstract. We identify the 2groupoid of deformations of a gerbe on a C ∞ manifold with the Deligne 2groupoid of a corresponding twist of the DGLA of local Hochschild cochains on C ∞ functions.
LOCAL MIDPOINTS ON SMOOTH MANIFOLDS
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
DEFORMATIONAL STRUCTURES ON SMOOTH MANIFOLDS
, 2002
"... Abstract deformational structures, in many aspects generalizing standard elasticity theory, are investigated. Within free deformational structures we define algebra of deformations, classify them by its special properties, define motions and conformal motions together with deformational decompositio ..."
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decomposition of manifolds, generalizing isometry of Riemannian spaces and consider some physical examples. In frame of dynamical deformational structures we formulate variational procedure for evolutional and static cases together with boundary conditions, derive dynamical (equilibrium in static case
The Degree of Symmetry of Certain Compact Smooth Manifolds II
, 2005
"... In this paper, we give the sharp estimates for the degree of symmetry and the semisimple degree of symmetry of certain four dimensional fiber bundles by virtue of the rigidity theorem of harmonic maps due to Schoen and Yau. As a corollary of this estimate, we compute the degree of symmetry and the ..."
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Cited by 3 (0 self)
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and the semisimple degree of symmetry of CP 2 × V, where V is closed smooth manifold admitting a real analytic Riemannian metric of nonpositive curvature. In addition, by the Albanese map, we obtain the sharp estimate of the degree of symmetry of a compact smooth manifold with some restrictions on its one
Equivariant Lefschetz maps for simplicial complexes and smooth manifolds
 Math. Ann
"... Abstract. Let X be a locally compact space with a continuous proper action of a locally compact group G. Assuming that X satisfies a certain kind of duality in equivariant bivariant Kasparov theory, we can enrich the classical construction of Lefschetz numbers for selfmaps to an equivariant Khomol ..."
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Cited by 4 (4 self)
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homology class. We compute the Lefschetz invariants for selfmaps of finitedimensional simplicial complexes and smooth manifolds. The resulting invariants are independent of the extra structure used to compute them. Since smooth manifolds can be triangulated, we get two formulas for the same Lefschetz invariant
Results 1  10
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130,905