2,630,752 research outputs found
1-loop graphs and configuration space integral for embedding spaces
We will construct differential forms on the embedding spaces Emb(R^j,R^n) for
n-j>=2 using configuration space integral associated with 1-loop graphs, and
show that some linear combinations of these forms are closed in some
dimensions. There are other dimensions in which we can show the closedness if
we replace Emb(R^j,R^n) by fEmb(R^j,R^n), the homotopy fiber of the inclusion
Emb(R^j,R^n) -> Imm(R^j,R^n). We also show that the closed forms obtained give
rise to nontrivial cohomology classes, evaluating them on some cycles of
Emb(R^j,R^n) and fEmb(R^j,R^n). In particular we obtain nontrivial cohomology
classes (for example, in H^3(Emb(R^2,R^5))) of higher degrees than those of the
first nonvanishing homotopy groups.Comment: 35 pages, to appear in Mathematical Proceedings of the Cambridge
Philosophical Societ
The SuperCOSMOS Sky Survey. Paper III: Astrometry
In this, the third in a series of three papers concerning the SuperCOSMOS Sky
Survey, we describe the astrometric properties of the database. We describe the
algorithms employed in the derivation of the astrometric parameters of the
data, and demonstrate their accuracies by comparison with external datasets
using the first release of data, the South Galactic Cap survey. We show that
the celestial coordinates, which are tied to the International Celestial
Reference Frame via the Tycho-2 reference catalogue, are accurate to better
than +/- 0.2 arcsec at J,R=19,18 rising to +/- 0.3 arcsec at J,R=22,21 with
positional dependent systematic effects from bright to faint magnitudes at the
+/- 0.1 arcsec level. The proper motion measurements are shown to be accurate
to typically +/- 10 mas/yr at J,R=19,18 rising to +/- 50 mas/yr at J,R=22,21
and are tied to zero using the extragalactic reference frame. We show that the
zeropoint errors in the proper motions are 17 and are no
larger than 10 mas/yr for R < 17 mas/yr.Comment: 15 pages, 12 figures; accepted for publication in MNRA
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