There are several approaches to summarizing a mathematician’s research accomplishments, and each has its advantages and disadvantages. This article is based upon a talk given at Tulane that was aimed at a fairly general audience, including faculty members in other areas and graduate students who had taken the usual entry level courses. As such, it is meant to be relatively nontechnical and to emphasize qualitative rather than quantitative issues; in keeping with this aim, references will be given for some standard topological notions that are not normally treated in entry level graduate courses. Since this was an hour talk, it was also not feasible to describe every single piece of published mathematical work that Terry Lawson has ever written; in particular, some papers like [42] and [50] would require lengthy digressions that are not easily related to the central themes in his main lines of research. Instead, we shall focus on some ways in which Terry’s work relates to an important thread in geometric topology; namely, the passage from studying problems in a given dimension to studying problems in the next dimensions. Qualitatively speaking, there are fairly well-developed theories for very low dimensions and for all sufficiently large dimensions, but between these ranges there are some dimensions in which the answers to many fundamental

Abstract. Recall that a pseudofree group action on a space X is one whose set of singular orbits forms a discrete subset of its orbit space. Equivalently – when G is finite and X is compact – the set of singular points in X is finite. In this paper, we classify all of the finite groups which admit pseudofree actions on S 2 × S 2. The groups are exactly those which admit orthogonal pseudofree actions on S 2 ×S 2 ⊂ R 3 × R 3, and they are explicitly listed. This paper can be viewed as a companion to a preprint of Edmonds, which uniformly treats the case in which the second Betti number of a four-manifold M is at least three. 1.

Abstract. Let X be a smooth closed oriented non-spin 4-manifold with even intersection form kE8⊕nH. In this article we show that we should have n ≥ |k | on X. Thus we confirm the 10-conjecture affirmatively. As an application, we also give an estimate of intersection 8 forms of spin coverings of non-spin 4-manifolds with even intersection forms. 1.