6,425 research outputs found

### Homotopy theory of bundles with fiber matrix algebra

In the present paper we consider a special class of locally trivial bundles
with fiber a matrix algebra. On the set of such bundles over a finite
$CW$-complex we define a relevant equivalence relation. The obtained stable
theory gives us a geometric description of the H-space structure \BSU_\otimes
on \BSU related to the tensor product of virtual \SU-bundles of virtual
dimension 1.Comment: This is a version of the paper published as a preprint of Max Planck
Institute for Mathematics. Several misprints are corrected. 24 page

### On radio emission of the Geminga pulsar and RBS 1223 at the frequency of 111 MHz

I have searched for pulsed radio emission from the Geminga pulsar and for the
nearby isolated neutron star 1RX J1308.6+2127 (RBS 1223) at the frequency of
111 MHz. No pulsed signals were detected from these sources. Upper limits for
mean flux density are 0.4 - 4 mJy for the Geminga pulsar and 1.5 - 15 mJy for
RBS 1223 depending on assumed duty cycle (.05 - .5) of the pulsars.Comment: 4 pages, 3 figure

### Formal groups over Hopf algebras

In this paper we study some generalization of the notion of a formal group
over ring, which may be called a formal group over Hopf algebra (FGoHA). The
first example of FGoHA was found under the study of cobordism's ring of some
$H$-space $\hat{Gr}$. The results, which are represented in this paper, show
that some constructions of the theory of formal group may be generalized to
FGoHA. For example, if ${\frak F}(x\otimes 1,1\otimes x) \in
(H{\mathop{\hat{\otimes}}\limits_R}H)[[x\otimes 1,1\otimes x]]$ is a FGoHA over
a Hopf algebra $(H,\mu,\nu, \Delta,\epsilon, S)$ over a ring $R$ without
torsion, then there exists a logarithm, i.e. the formal series ${\frak g}(x)\in
H_\mathbb{Q}[[x]]$ such that $(\Delta {\frak g})({\frak F}(x\otimes 1,1\otimes
x))= {\frak c}+{\frak g}(x)\otimes 1+1\otimes {\frak g}(x),$ where {\frak
c}\in H_\mathbb{Q}{\mathop{\hat{\otimes}}\limits_{R_ \mathbb{Q}}}H_\mathbb{Q},
(\id \otimes \epsilon){\frak c}=0=(\epsilon \otimes \id){\frak c} and (\id
\otimes \Delta){\frak c}+1\otimes {\frak c}-(\Delta \otimes \id){\frak
c}-{\frak c}\otimes 1=0 (recall that the last condition means that ${\frak c}$
is a cocycle in the cobar complex of the Hopf algebra $H_\mathbb{\mathbb{Q}}$).
On the other hand, FGoHA have series of new properties. For example, the
convolution on a Hopf algebra allows us to get new FGoHA from given.Comment: 21page

### On $K$-theory automorphisms related to bundles of finite order

In the present paper we describe the action of (not necessarily line) bundles
of finite order on the $K$-functor in terms of classifying spaces. This
description might provide with an approach for more general twistings in
$K$-theory than ones related to the action of the Picard group.Comment: 18 page

### Logarithms of formal groups over Hopf algebras

The aim of this paper is to prove the following result. For any commutative
formal group ${\frak F}(x\otimes 1,1\otimes x),$ which is considered as a
formal group over $H_\mathbb{Q},$ there exists a homomorphism to a formal group
of the form ${\frak c}+x\otimes 1+1\otimes x,$ where $\frak c\in
H_\mathbb{Q}{\mathop{\hat{\otimes}} \limits_{R_\mathbb{Q}}}H_\mathbb{Q}$ such
that (\id \otimes \epsilon){\frak c}=0= (\epsilon \otimes \id){\frak c}.Comment: 5 page

### A generalization of the topological Brauer group

In the present paper we study some homotopy invariants which can be defined
by means of bundles with fiber a matrix algebra. We also introduce some
generalization of the Brauer group in the topological context and show that any
its element can be represented as a locally trivial bundle with a group of
invertible operators in a Hilbert space as the structure group. Finally, we
discuss its possible applications in the twisted $K$-theory.Comment: 34 pages. v5: The part concerning the generalized Brauer group has
been completely rewritten. An application to twisted $K$-theory is adde

### Topological obstructions to embedding of a matrix algebra bundle into a trivial one

In the present paper we describe topological obstructions to embedding of a
(complex) matrix algebra bundle into a trivial one under some additional
arithmetic condition on their dimensions. We explain a relation between this
problem and some principal bundles with structure groupoid. Finally, we briefly
discuss a relation of our results to the twisted K-theory.Comment: v.14: 29 pages, corrections and additions in Section

### Supplement to the paper "Floating bundles and their applications"

This paper is the supplement to the section 2 of the paper "Floating bundles
and their applications" (math.AT/0102054). Below we construct the denumerable
set of extensions of the formal group of geometric cobordisms $F(x\otimes
1,1\otimes x)$ by the Hopf algebra $H=\Omega_U^*(Gr).$Comment: 4 pages, xypi

### On scattering of Giant Pulses from the Crab Pulsar: a Scattering Function

Simultaneous dual-frequency observations of giant pulses from the Crab pulsar
were performed at the frequencies of 61 and 111 MHz. It is shown that
scattering of giant pulses from the Crab pulsar occurs at thick, and not at
thin screen.Comment: 3 pages, 3 figure

### A bordism theory related to matrix Grassmannians

In the present paper we study a bordism theory related to pairs $(M,\, \xi),$
where $M$ is a closed smooth oriented manifold with a stably trivial normal
bundle and $\xi$ is a virtual \SU-bundle of virtual dimension 1 over $M$. The
main result is the calculation of the corresponding ring modulo torsion and the
explicit description of its generators.Comment: 10 page

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