Double node neighborhoods and families of simply connected 4-manifolds with b^+=1

We introduce a new technique that is used to show that the complex projective plane blown up at 6, 7, or 8 points has infinitely many distinct smooth structures. None of these smooth structures admit smoothly embedded spheres with self-intersection -1, i.e. they are minimal. In addition, none these smooth structures admit an underlying symplectic structure. Shortly after the appearance of a preliminary version of this article, Park, Stipsicz, and Szabo used the techniques described herein to show that the complex projective plane blown up at 5 points has infinitely many distinct smooth structures. In the final section of this paper we give a somewhat different construction of such a family of examples.Comment: 11 pages, More typos and minor errors correcte

Knots, Links, and 4-Manifolds

In this paper we investigate the relationship between isotopy classes of knots and links in S^3 and the diffeomorphism types of homeomorphic smooth 4-manifolds. As a corollary of this initial investigation, we begin to uncover the surprisingly rich structure of diffeomorphism types of manifolds homeomorphic to the K3 surface.Comment: 31 page

Unemployment Insurance, Duration of Unemployment, and Subsequent Wage Gain

[Excerpt] In order to evaluate what the optimal level of UI benefits is, one must therefore first estimate the magnitude of the relationships between UI benefits levels and unemployed workers\u27 durations of unemployment and post-unemployment wages. There have been several previous studies of the impact of UI benefits on duration of spells of unemployment, however none have been completely satisfactory methodologically. To our knowledge, there have been no previous studies of the system\u27s impact on subsequent wage rates. We attempt to fill these gaps, utilizing data from the National Longitudinal Survey (NLS) to estimate both relationships. The plan of our paper is as follows. First, we sketch the implications of theories of job search for our estimating equations. Next, we briefly discuss the NLS data. The following four sections summarize the empirical results we have obtained for four cohorts of data: older males, ages 45-59; women, ages 30-44; and younger males and females, ages 14-24. Finally, we consider the implications of our results for public policy. Due to space limitations our discussion here is necessarily brief and details of our research are found elsewhere