Microtubule flux in spindles of insect spermatocytes, long-used models for studies on chromosome behavior during meiosis, was revealed after iontophoretic microinjection of rhodamine-conjugated (rh)-tubulin and fluorescent speckle microscopy. In time-lapse movies of crane-fly spermtocytes, fluorescent speckles generated when rh-tubulin incorporated at microtubule plus ends moved poleward through each half-spindle and then were lost from microtubule minus ends at the spindle poles. The average poleward velocity of approximately 0.7 microm/min for speckles within kinetochore microtubules at metaphase increased during anaphase to approximately 0.9 microm/min. Segregating half-bivalents had an average poleward velocity of approximately 0.5 microm/min, about half that of speckles within shortening kinetochore fibers. When injected during anaphase, rhtubulin was incorporated at kinetochores, and kinetochore fiber fluorescence spread poleward as anaphase progressed. The results show that tubulin subunits are added to the plus end of kinetochore microtubules and are removed from their minus ends at the poles, all while attached chromosomes move poleward during anaphase A. The results cannot be explained by a Pac-man model, in which 1) kinetochore-based, minus end-directed motors generate poleward forces for anaphase A and 2) kinetochore microtubules shorten at their plus ends. Rather, in these cells, kinetochore fiber shortening during anaphase A occurs exclusively at the minus ends of kinetochore microtubules.
In this paper we classify Legendrian and transverse knots in the knot types
obtained from positive torus knots by cabling. This classification allows us to
demonstrate several new phenomena. Specifically, we show there are knot types
that have non-destabilizable Legendrian representatives whose
Thurston-Bennequin invariant is arbitrarily far from maximal. We also exhibit
Legendrian knots requiring arbitrarily many stabilizations before they become
Legendrian isotopic. Similar new phenomena are observed for transverse knots.
To achieve these results we define and study "partially thickenable" tori,
which allow us to completely classify solid tori representing positive torus
knots.Comment: 34 pages, 6 figure
We prove that the class of topological knot types that are both Legendrian
simple and satisfy the uniform thickness property (UTP) is closed under
cabling. An immediate application is that all iterated cabling knot types that
begin with negative torus knots are Legendrian simple. We also examine, for
arbitrary numbers of iterations, iterated cablings that begin with positive
torus knots, and establish the Legendrian simplicity of large classes of these
knot types, many of which also satisfy the UTP. In so doing we obtain new
necessary conditions for both the failure of the UTP and Legendrian
non-simplicity in the class of iterated torus knots, including specific
conditions on knot types.Comment: 21 pages, 5 figures; final version, to appear in Algebraic and
Geometric Topolog
Abstract. We show that after stabilizations of opposite parity and braid isotopy, any two braids in the same topological link type cobound embedded annuli. We use this to prove the generalized Jones conjecture relating the braid index and algebraic length of closed braids within a link type, following a reformulation of the problem by Kawamuro.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.