27,271 research outputs found
Fat handles and phase portraits of Non Singular Morse-Smale flows on S^3 with unknotted saddle orbits
In this paper we build Non-singular Morse-Smale flows on S^3 with unknotted
and unlinked saddle orbits by identifying fat round handles along their
boundaries. This way of building the flows enables to get their phase
portraits. We also show that the presence of heteroclinic trajectories imposes
an order in the round handle decomposition of these flows; this order is total
for NMS flows composed of one repulsive, one attractive and n unknotted saddle
orbits, for n >1.Comment: 15 page
Arcs on Determinantal Varieties
We study arc spaces and jet schemes of generic determinantal varieties. Using
the natural group action, we decompose the arc spaces into orbits, and analyze
their structure. This allows us to compute the number of irreducible components
of jet schemes, log canonical thresholds, and topological zeta functions.Comment: 27 pages. This is part of the author's PhD thesis at the University
of Illinois at Chicago. v2: Minor changes. To appear in Transactions of the
American Mathematical Societ
Filling of closed Surfaces
Let denote a closed oriented surface of genus . A set of simple
closed curves is called a filling of if its complement is a disjoint
union of discs. The mapping class group of genus acts on
the set of fillings of . The union of the curves in a filling forms a
graph on the surface which is a so-called decorated fat graph. It is a fact
that two fillings of are in the same -orbit if and only
if the corresponding fat graphs are isomorphic. We prove that any filling of
whose complement is a single disc (i.e., a so-called minimal filling) has
either three or four closed curves and in each of these two cases, there is a
unique such filling up to the action of .
We provide a constructive proof to show that the minimum number of discs in
the complement of a filling pair of is two. Finally, given positive
integers and with , we construct a filling pair of
such that the complement is a union of topological discs.Comment: 15 Pages, 11 Figures, To appear in J. Topol. Ana
Imaging of adult ocular and orbital pathology - a pictorial review
Orbital pathology often presents a diagnostic challenge to the reporting radiologist. The aetiology is protean, and clinical input is therefore often necessary to narrow the differential diagnosis. With this manuscript, we provide a pictorial review of adult ocular and orbital pathology.peer-reviewe
On the backreaction of frame dragging
The backreaction on black holes due to dragging heavy, rather than test,
objects is discussed. As a case study, a regular black Saturn system where the
central black hole has vanishing intrinsic angular momentum, J^{BH}=0, is
considered. It is shown that there is a correlation between the sign of two
response functions. One is interpreted as a moment of inertia of the black ring
in the black Saturn system. The other measures the variation of the black ring
horizon angular velocity with the central black hole mass, for fixed ring mass
and angular momentum. The two different phases defined by these response
functions collapse, for small central black hole mass, to the thin and fat ring
phases. In the fat phase, the zero area limit of the black Saturn ring has
reduced spin j^2>1, which is related to the behaviour of the ring angular
velocity. Using the `gravitomagnetic clock effect', for which a universality
property is exhibited, it is shown that frame dragging measured by an
asymptotic observer decreases, in both phases, when the central black hole mass
increases, for fixed ring mass and angular momentum. A close parallelism
between the results for the fat phase and those obtained recently for the
double Kerr solution is drawn, considering also a regular black Saturn system
with J^{BH}\neq 0.Comment: 18 pages, 8 figure
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