391 research outputs found
Knot Floer homology detects fibred knots
Ozsv\'ath and Szab\'o conjectured that knot Floer homology detects fibred
knots in . We will prove this conjecture for null-homologous knots in
arbitrary closed 3--manifolds. Namely, if is a knot in a closed 3--manifold
, is irreducible, and is monic, then is fibred.
The proof relies on previous works due to Gabai, Ozsv\'ath--Szab\'o, Ghiggini
and the author. A corollary is that if a knot in admits a lens space
surgery, then the knot is fibred.Comment: version 4: incorporates referee's suggestions, to appear in
Inventiones Mathematica
Innovative Strategies for Drug Delivery to the Ocular Posterior Segment
Innovative and new drug delivery systems (DDSs) have recently been developed to vehicle treatments and drugs to the ocular posterior segment and the retina. New formulations and technological developments, such as nanotechnology, novel matrices, and non-traditional treatment strategies, open new perspectives in this field. The aim of this mini-review is to highlight promising strategies reported in the current literature based on innovative routes to overcome the anatomical and physiological barriers of the vitreoretinal structures. The paper also describes the challenges in finding appropriate and pertinent treatments that provide safety and efficacy and the problems related to patient compliance, acceptability, effectiveness, and sustained drug delivery. The clinical application of these experimental approaches can help pave the way for standardizing the use of DDSs in developing enhanced treatment strategies and personalized therapeutic options for ocular pathologies
The size of triangulations supporting a given link
Let T be a triangulation of S^3 containing a link L in its 1-skeleton. We
give an explicit lower bound for the number of tetrahedra of T in terms of the
bridge number of L. Our proof is based on the theory of almost normal surfaces.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol5/paper13.abs.htm
Promoting Essential Laminations
We show that every co--orientable taut foliation F of an orientable,
atoroidal 3-manifold admits a transverse essential lamination. If this
transverse lamination is a foliation G, the pair F,G are the unstable and
stable foliation respectively of an Anosov flow. Otherwise, F admits a pair of
transverse very full genuine laminations.
In the second case, M satisfies the weak geometrization conjecture - either
its fundamental group contains Z+Z or it is word-hyperbolic. Moreover, if M is
atoroidal, the mapping class group of M is finite, and any automorphism
homotopic to the identity is isotopic to the identity.Comment: 56 pages, 11 figures; version 3: final version, incorporates
referee's suggestion
Thin presentation of knots and lens spaces
This paper concerns thin presentations of knots K in closed 3-manifolds M^3
which produce S^3 by Dehn surgery, for some slope gamma. If M does not have a
lens space as a connected summand, we first prove that all such thin
presentations, with respect to any spine of M have only local maxima. If M is a
lens space and K has an essential thin presentation with respect to a given
standard spine (of lens space M) with only local maxima, then we show that K is
a 0-bridge or 1-bridge braid in M; furthermore, we prove the minimal
intersection between K and such spines to be at least three, and finally, if
the core of the surgery K_gamma yields S^3 by r-Dehn surgery, then we prove the
following inequality: |r| <= 2g, where g is the genus of K_gamma.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-23.abs.htm
Recent Developments in Gene Therapy for Neovascular Age-Related Macular Degeneration: A Review
Age-related macular degeneration (AMD) is a complex and multifactorial disease and a leading cause of irreversible blindness in the elderly population. The anti-vascular endothelial growth factor (anti-VEGF) therapy has revolutionized the management and prognosis of neovascular AMD (nAMD) and is currently the standard of care for this disease. However, patients are required to receive repeated injections, imposing substantial social and economic burdens. The implementation of gene therapy methods to achieve sustained delivery of various therapeutic proteins holds the promise of a single treatment that could ameliorate the treatment challenges associated with chronic intravitreal therapy, and potentially improve visual outcomes. Several early-phase trials are currently underway, evaluating the safety and efficacy of gene therapy for nAMD; however, areas of controversy persist, including the therapeutic target, route of administration, and potential safety issues. In this review, we assess the evolution of gene therapy for nAMD and summarize several preclinical and early-stage clinical trials, exploring challenges and future directions
3-manifolds which are spacelike slices of flat spacetimes
We continue work initiated in a 1990 preprint of Mess giving a geometric
parameterization of the moduli space of classical solutions to Einstein's
equations in 2+1 dimensions with cosmological constant 0 or -1 (the case +1 has
been worked out in the interim by the present author). In this paper we make a
first step toward the 3+1-dimensional case by determining exactly which closed
3-manifolds M^3 arise as spacelike slices of flat spacetimes, and by finding
all possible holonomy homomorphisms pi_1(M^3) to ISO(3,1).Comment: 10 page
Homogeneous links, Seifert surfaces, digraphs and the reduced Alexander polynomial
We give a geometric proof of the following result of Juhasz. \emph{Let
be the leading coefficient of the Alexander polynomial of an alternating knot
. If then has a unique minimal genus Seifert surface.} In
doing so, we are able to generalise the result, replacing `minimal genus' with
`incompressible' and `alternating' with `homogeneous'. We also examine the
implications of our proof for alternating links in general.Comment: 37 pages, 28 figures; v2 Main results generalised from alternating
links to homogeneous links. Title change
Decoupling Inflation From the String Scale
When Inflation is embedded in a fundamental theory, such as string theory, it
typically begins when the Universe is already substantially larger than the
fundamental scale [such as the one defined by the string length scale]. This is
naturally explained by postulating a pre-inflationary era, during which the
size of the Universe grew from the fundamental scale to the initial
inflationary scale. The problem then arises of maintaining the [presumed]
initial spatial homogeneity throughout this era, so that, when it terminates,
Inflation is able to begin in its potential-dominated state. Linde has proposed
that a spacetime with compact negatively curved spatial sections can achieve
this, by means of chaotic mixing. Such a compactification will however lead to
a Casimir energy, which can lead to effects that defeat the purpose unless the
coupling to gravity is suppressed. We estimate the value of this coupling
required by the proposal, and use it to show that the pre-inflationary
spacetime is stable, despite the violation of the Null Energy Condition
entailed by the Casimir energy.Comment: 24 pages, 5 eps figures, references added, stylistic changes, version
to appear in Classical and Quantum Gravit
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