2,832 research outputs found
Hypertoric manifolds of infinite topological type
We analyse properties of hypertoric manifolds of infinite topological type,
including their topology and complex structures. We show that our manifolds
have the homotopy type of an infinite union of compact toric varieties. We also
discuss hypertoric analogues of the periodic Ooguri-Vafa spaces
Are hygiene standards useful in assessing infection risk?
We monitored the surface level cleanliness of a five-bedded surgical intensive care unit (SICU) over a ten-week period in order to evaluate proposed hygiene standards.Ten environmental sites within SICU were sampled twice weekly along with collection of clinical and patient activity data. The standards designate aerobic colony counts (ACCs) >2.5cfu/cm2 from hand-touch sites and the presence of Staphylococcus aureus as hygiene failures. Nearly a quarter of 200 samples failed the standards, mostly from hand-touch sites on curtains, beds and medical equipment. The total number of fails each week was associated with bed occupancy (p=0.04), trending towards association with SICU-acquired infections (p=0.11). Environmental S.aureus was associated with the proportion of beds occupied (p = 0.02). Indistinguishable genotypes were found between patient and environmental staphylococci, with timescales supporting staphylococcal transmission in both directions. Hygiene standards based on microbial growth levels and the presence of S.aureus reflect patient activity and provide a means to risk manage infection. They also exposed a staphylococcal reservoir that could represent a more tangible risk to patients. Standards for surface level cleanliness deserve further evaluation
A multiplicative analogue of complex symplectic implosion
We introduce a multiplicative version of complex-symplectic implosion in the
case of SL(n, \C).
The universal multiplicative implosion for SL(n, \C) is an affine variety
and can be viewed as a nonreductive geometric invariant theory quotient. It
carries a torus action. and reductions by this action give the Steinberg fibres
of SL(n, \C). We also explain how the real symplectic group-valued universal
implosion introduced by Hurtubise, Jeffrey and Sjamaar may be identified inside
this space.Comment: To appear in European Journal of Mathematic
Toric Hypersymplectic Quotients
We study the hypersymplectic spaces obtained as quotients of flat
hypersymplectic space R^{4d} by the action of a compact Abelian group. These
4n-dimensional quotients carry a multi-Hamilitonian action of an n-torus. The
image of the hypersymplectic moment map for this torus action may be described
by a configuration of solid cones in R^{3n}. We give precise conditions for
smoothness and non-degeneracy of such quotients and show how some properties of
the quotient geometry and topology are constrained by the combinatorics of the
cone configurations. Examples are studied, including non-trivial structures on
R^{4n} and metrics on complements of hypersurfaces in compact manifolds.Comment: 26 pages, 6 figures, small linguistic correction
On Spin(7) holonomy metric based on SU(3)/U(1)
We investigate the holonomy metric of cohomogeneity one with the
principal orbit . A choice of U(1) in the two dimensional Cartan
subalgebra is left as free and this allows manifest (= the
Weyl group) symmetric formulation. We find asymptotically locally conical (ALC)
metrics as octonionic gravitational instantons. These ALC metrics have orbifold
singularities in general, but a particular choice of the U(1) subgroup gives a
new regular metric of holonomy. Complex projective space that is a supersymmetric four-cycle appears as a singular orbit. A
perturbative analysis of the solution near the singular orbit shows an evidence
of a more general family of ALC solutions. The global topology of the manifold
depends on a choice of the U(1) subgroup. We also obtain an -normalisable
harmonic 4-form in the background of the ALC metric.Comment: 21 pages, Latex, Introduction slightly expanded, an error in section
6 corrected and references added, (v3) minor correction
On the nonexistence of quasi-Einstein metrics
We study complete Riemannian manifolds satisfying the equation by studying the associated PDE for . By developing a gradient estimate for , we show
there are no nonconstant solutions. We then apply this to show that there are
no nontrivial Ricci flat warped products with fibers which have nonpositive
Einstein constant. We also show that for nontrivial steady gradient Ricci
solitons, the quantity is a positive constant.Comment: Final version: Improved exposition of Section 2, corrected minor
typo
- …