6,188 research outputs found
Having the H-space structure is not a generic property
In this note, we answer in negative a question posed by McGibbon about the
generic property of H-space structure.
In fact we verify the conjecture of Roitberg. Incidentally, the same example
also answers in negative the open problem 10 in McGibbon
Equivariant Phantom maps
A successful generalization of phantom map theory to the equivariant case for
all compact Lie groups is obtained in this paper.
One of the key observations is the discovery of the fact that homotopy fiber
of equivariant completion splits as product of equivariant Eilenberg-Maclane
spaces which seems impossible at first sight by the example of Triantafillou
Rational homotopy theory and nonnegative curvature
In this note, we answer positively a question by Belegradek and Kapovitch
about the relation between rational homotopy theory and a problem in Riemannian
geometry which asks that total spaces of which vector bundles over compact
nonnegative curved manifolds admit (complete) metrics with nonnegative
curvature.Comment: 7 pages, talk to be given at SISTAG, National Univ. of Singapore,
Jul.2-6, 200
A General Stochastic Maximum Principle For Optimal Control Of Stochastic Systems Driven By Multidimensional Teugel's Martingales
A necessary maximum principle is proved for optimal controls of stochastic
systems driven by multidimensional Teugel's martingales. The multidimensional
Teugel's martingales are constructed by orthogonalizing the multidimensional
L\'{e}vy processes. The control domain need not be convex, and the control is
allowed to enter into the terms of Teugel's martingales
Classification of the congruence classes of with 2-torsion free homology
In this paper, we classify the congruence classes of
-polyhedra, i.e. -connected, at most
-dimensional polyhedra with 2-torsion free homology. The proof relies on
the matrix problem technique which was developed in the classification of
representations of algebras and applied to homotopy theory by Baues and Drozd.Comment: This article is accepted by SCIENCE CHINA Mathematics. arXiv admin
note: text overlap with arXiv:1509.0793
An Algorithm for Reducing Approximate Nearest Neighbor to Approximate Near Neighbor with O(logn) Query Time
This paper proposes a new algorithm for reducing Approximate Nearest Neighbor
problem to Approximate Near Neighbor problem. The advantage of this algorithm
is that it achieves O(log n) query time. As a reduction problem, the uery time
complexity is the times of invoking the algorithm for Approximate Near Neighbor
problem. All former algorithms for the same reduction need polylog(n) query
time. A box split method proposed by Vaidya is used in our paper to achieve the
O(log n) query time complexity
The decomposability of smash product of A_n^2-complexes
In this paper, we determine the decomposability of smash product of two
indecomposable A_n^2-complexes, i.e., (n-1)-connected finite CW-complexes with
dimension at most n+2 (n\geq 3)
Toroidal orbifolds, gerbes and group cohomology
We compute the integral cohomology of certain semi-direct products arising
from a linear G-action on the n-torus, where G is a finite group. The main
application is the complete calculation of torsion gerbes for certain six
dimensional examples arising from string theory
The stable homotopy classification of -connected -dimensional polyhedra with 2 torsion free homology
In this paper, we study the stable homotopy types of
-polyhedra, i.e., -connected, at most
-dimensional polyhedra with 2-torsion free homologies. We are able to
classify the indecomposable -polyhedra. The proof relies
on the matrix problem technique which was developed in the classification of
representaions of algebras and applied to homotopy theory by Baues and Drozd
Secondary Brown-Kervaire Quadratic forms and -manifolds
In this paper we define a secondary Brown-Kervaire quadratic forms. Among the
applications we obtain a complete classification of (n-2)-connected
2n-dimensional framed manifolds up to homeomorphism and homotopy equivalence, .
In particular, we prove that the homotopy type of such manifolds determine
their homeomorphism type
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