Whitney tower concordance of classical links

This paper computes Whitney tower filtrations of classical links. Whitney towers consist of iterated stages of Whitney disks and allow a tree-valued intersection theory, showing that the associated graded quotients of the filtration are finitely generated abelian groups. Twisted Whitney towers are studied and a new quadratic refinement of the intersection theory is introduced, measuring Whitney disk framing obstructions. It is shown that the filtrations are completely classified by Milnor invariants together with new higher-order Sato-Levine and higher-order Arf invariants, which are obstructions to framing a twisted Whitney tower in the 4-ball bounded by a link in the 3-sphere. Applications include computation of the grope filtration, and new geometric characterizations of Milnor's link invariants.Comment: Only change is the addition of this comment: This paper subsumes the entire preprint "Geometric Filtrations of Classical Link Concordance" (arXiv:1101.3477v2 [math.GT]) and the first six sections of the preprint "Universal Quadratic Forms and Untwisting Whitney Towers" (arXiv:1101.3480v2 [math.GT]

Study of magnetic annular plasma accelerator Summary report, 15 Apr. 1964 - 14 Jan. 1966

Magnetic annular arc for achieving high propulsive efficiencie

Homotopy versus isotopy: spheres with duals in 4-manifolds

David Gabai recently proved a smooth 4-dimensional "Light Bulb Theorem" in the absence of 2-torsion in the fundamental group. We extend his result to 4-manifolds with arbitrary fundamental group by showing that an invariant of Mike Freedman and Frank Quinn gives the complete obstruction to "homotopy implies isotopy" for embedded 2-spheres which have a common geometric dual. The invariant takes values in an Z/2Z-vector space generated by elements of order 2 in the fundamental group and has applications to unknotting numbers and pseudo-isotopy classes of self-diffeomorphisms. Our methods also give an alternative approach to Gabai's theorem using various maneuvers with Whitney disks and a fundamental isotopy between surgeries along dual circles in an orientable surface

Prevalence and correlates of mild cognitive impairment among diverse Hispanics/Latinos: Study of Latinos-Investigation of Neurocognitive Aging results.

IntroductionWe estimated the prevalence and correlates of mild cognitive impairment (MCI) among middle-aged and older diverse Hispanics/Latinos.MethodsMiddle-aged and older diverse Hispanics/Latinos enrolled (n = 6377; 50-86 years) in this multisite prospective cohort study were evaluated for MCI using the National Institute on Aging-Alzheimer's Association diagnostic criteria.ResultsThe overall MCI prevalence was 9.8%, which varied between Hispanic/Latino groups. Older age, high cardiovascular disease (CVD) risk, and elevated depressive symptoms were significant correlates of MCI prevalence. Apolipoprotein E4 (APOE) and APOE2 were not significantly associated with MCI.DiscussionMCI prevalence varied among Hispanic/Latino backgrounds, but not as widely as reported in the previous studies. CVD risk and depressive symptoms were associated with increased MCI, whereas APOE4 was not, suggesting alternative etiologies for MCI among diverse Hispanics/Latinos. Our findings suggest that mitigating CVD risk factors may offer important pathways to understanding and reducing MCI and possibly dementia among diverse Hispanics/Latinos