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In a recent paper we defined a new filtration of the mapping class group – the Lagrangian filtration. We here determine the successive quotients of this filtration, up to finite index. As an application we show that, for any additive invariant of finite-type (e.g. the Casson invariant) and any level of the Lagrangian filtration, there is a homology 3-sphere which has a Heegaard decomposition whose gluing diffeomorphism lies at that level, on which this invariant is non-zero. In a final section we examine the relationship between the Johnson and Lagrangian filtrations.
The present paper is a continuation of [Ga],
[GL1] and [GO]. Using a key lemma
we compare two currently existing definitions of finite type invariants
integral homology spheres and show that type 3m invariants in
the sense of
Ohtsuki [Oh] are included in type m invariants
the sense of the first author [Ga].
This partially answers question 1 of [Ga]. We
show that type 3m invariants of
integral homology spheres in the sense of Ohtsuki map to type 2m
invariants of knots in S3, thus answering question
2 from [Ga].
An ultra-high vacuum chamber designed for in situ grazing incidence small angle x-ray scattering (GISAXS) surface analysis is described. Unique features of this equipment are the precision rotary feedthrough for angular alignment of the sample, the sample heating design, the Be window arrangement, and the compatibility of this chamber with both a rotating anode and a synchrotron beamline. This chamber was used as part of a GISAXS camera utilizing a 18 kW Rigaku rotating anode, pin-hole collimation, and a position sensitive detector. The resolution of this camera was 0.007 A-1 with a 1.4 mm wide beamstop and CuKα
The physiological response to stress falls mainly on the cardiovascular system, adrenergic stimulation resulting in peripheral vasoconstriction and an increase in systemic blood pressure. The analogous effects that occur in anxiety-provoking situations immediately suggest an association, whether causal or effectual, between raised blood pressure and anxiety. It has also been suggested that hypertensive individuals exhibit more aggressive traits than others and that these may be hidden or suppressed, becoming manifest by abnormal elevation of the blood pressure (Smirk, 1957).
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