243 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
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
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)
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
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
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
Mislin genus of maps
In this paper, we prove that the Mislin genus of a (co-)H-map between
(co-)H-spaces under certain natural conditions is a finite abelian group which
generalizes results in Zabrodsky, McGibbon and HurvitzComment: 27 page
Gerbes and twisted orbifold quantum cohomology
In this article, we construct an orbifold quantum cohomology twisted by a
flat gerbe. Then we compute these invariants in the case of a smooth manifold
and a discrete torsion on a global quotient orbifold.Comment: Amste
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