275 research outputs found
Finiteness of -equivalence types of gauge groups
Let be a finite CW complex and a compact connected Lie group. We show
that the number of gauge groups of principal -bundles over is finite up
to -equivalence for . As an example, we give a lower bound of
the number of -equivalence types of gauge groups of principal
\SU(2)-bundles over .Comment: 17 pages, 10 figure
Mapping spaces from projective spaces
We denote the -th projective space of a topological monoid by
and the classifying space by . Let be a well-pointed topological monoid
of the homotopy type of a CW complex and a well-pointed grouplike
topological monoid. We prove the weak equivalence between the pointed mapping
space and the space of all -maps from to
. This fact has several applications. As the first application, we show
that the connecting map of the evaluation
fiber sequence
is
delooped. As other applications, we consider higher homotopy commutativity,
-types of gauge groups, -spaces by Iwase--Mimura--Oda--Yoon and
homotopy pullback of -maps. In particular, we show that the -space
and the -space are exactly the same concept and give some new examples
of -spaces.Comment: 26 pages, 3 figures; the appendix in v3 is deleted since its argument
was incomplet
Scattering Theory for the Dirac Equation with a Nonlocal Term
Consider a scattering problem for the Dirac equation with a nonlocal term including he Hartree type. We show the existence of scattering operators for small initial data n the subcritical and critical Sobolev spaces
On the asymptotic behavior of nonlinear waves in the presence of a short-range potential
Consider the nonlinear wave equation with zero mass and a time-independent otential in three space dimensions. When it comes to the associated Cauchy problem, it s already known that short-range potentials do not a®ect the existence of small-amplitude olutions. In this paper, we focus on the associated scattering problem and we show that he situation is quite di®erent there. In particular, we show that even arbitrarily small and apidly decaying potentials may a®ect the asymptotic behavior of solutions
Small-data scattering for nonlinear waves of critical decay in two space dimensions
Consider the nonlinear wave equation with zero mass in two space dimensions. hen it comes to the associated Cauchy problem with small initial data, the known existence esults are already sharp; those require the data to decay at a rate k ¸ kc, where kc is a critical ecay rate that depends on the order of the nonlinearity. However, the known scattering results reat only the supercritical case k > kc. In this paper, we prove the existence of the scattering perator for the full optimal range k ¸ kc
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