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

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

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

Some beautiful equations of mathematical physics

The basic ideas and the important role of gauge principles in modern elementary particle physics are outlined. There are three theoretically consistent gauge principles in quantum field theory: the spin-1 gauge principle of electromagnetism and the standard model, the spin-2 gauge principle of general relativity, and the spin-3/2 gauge principle of supergravity. (Dirac Prize lecture, November 1993. Two figures are unavailable, but should not be essential.)Comment: 18 page