56,552 research outputs found
Surgery and involutions on 4-manifolds
We prove that the canonical 4-dimensional surgery problems can be solved
after passing to a double cover. This contrasts the long-standing conjecture
about the validity of the topological surgery theorem for arbitrary fundamental
groups (without passing to a cover). As a corollary, the surgery conjecture is
reformulated in terms of the existence of free involutions on a certain class
of 4-manifolds. We consider this question and analyze its relation to the
A,B-slice problem.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-70.abs.htm
Subexponential groups in 4-manifold topology
We present a new, more elementary proof of the Freedman-Teichner result that
the geometric classification techniques (surgery, s-cobordism, and
pseudoisotopy) hold for topological 4-manifolds with groups of subexponential
growth. In an appendix Freedman and Teichner give a correction to their
original proof, and reformulate the growth estimates in terms of coarse
geometry.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol4/paper14.abs.htm
Universal quadratic forms and Whitney tower intersection invariants
The first part of this paper exposits a simple geometric description of the
Kirby-Siebenmann invariant of a 4--manifold in terms of a quadratic refinement
of its intersection form. This is the first in a sequence of higher-order
intersection invariants of Whitney towers studied by the authors, particularly
for the 4--ball.
In the second part of this paper, a general theory of quadratic forms is
developed and then specialized from the non-commutative to the commutative to
finally, the symmetric settings. The intersection invariant for twisted Whitney
towers is shown to be the universal symmetric refinement of the framed
intersection invariant. As a corollary we obtain a short exact sequence that
has been essential in the understanding of Whitney towers in the 4--ball.Comment: This paper subsumes the second half (Section 7) of the previously
posted paper "Universal Quadratic Forms and Untwisting Whitney Towers"
(http://arxiv.org/abs/1101.3480
Exponential separation in 4-manifolds
We use a new geometric construction, grope splitting, to give a sharp bound
for separation of surfaces in 4-manifolds. We also describe applications of
this technique in link-homotopy theory, and to the problem of locating
pi_1-null surfaces in 4-manifolds. In our applications to link-homotopy, grope
splitting serves as a geometric substitute for the Milnor group.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol4/paper13.abs.htm
Link groups of 4-manifolds
The notion of a Bing cell is introduced, and it is used to define invariants,
link groups, of 4-manifolds. Bing cells combine some features of both surfaces
and 4-dimensional handlebodies, and the link group \lambda(M) measures certain
aspects of the handle structure of a 4-manifold M. This group is a quotient of
the fundamental group, and examples of manifolds are given with \pi_1(M) not
equal to \lambda(M). The main construction of the paper is a generalization of
the Milnor group, which is used to formulate an obstruction to embeddability of
Bing cells into 4-space. Applications to the A-B slice problem and to the
structure of topological arbiters are discussed.Comment: 34 pages, 7 figures. v.3: minor phrasing change
Constrained Differential Renormalization of Yang-Mills Theories
We renormalize QCD to one loop in coordinate space using constrained
differential renormalization, and show explicitly that the Slavnov-Taylor
identities are preserved by this method.Comment: LaTex, 13 pages with 2 ps figure
ILR Impact Brief - Industry Clusters Affect Job Mobility and Earnings Growth
[Excerpt] Industry clusters are associated with greater job hopping and faster growth in workers’ earning power relative to the experience of workers at less spatially concentrated companies. Workers in these clusters tend to accept lower starting salaries than peers at more isolated firms in anticipation of rapid gains that accompany movement from job to job within the cluster and the accumulation of industry-specific knowledge. Higher earnings observed among workers in clustered firms may also reflect choices made by workers with certain characteristics to seek employment in an area with a high concentration of similar firms and by companies with certain characteristics to locate in such an area
New Face of Work Survey
Documents why Americans in their 50s and 60s plan to work longer than the previous generation. Includes attitudes about post-retirement work based on gender and race, and support for policy changes to remove obstacles to working past retirement age
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