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**1 - 4**of**4**### BETWEEN LOWER AND HIGHER DIMENSIONS (in the work of Terry Lawson)

"... 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 ..."

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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

### A ROKHLIN CONJECTURE AND SMOOTH QUOTIENTS BY THE COMPLEX CONJUGATION OF SINGULAR REAL ALGEBRAIC SURFACES

, 1999

"... 1.1. A Rokhlin Conjecture and its variations. Considering real algebraic varieties, I use prefixes C and R to denote their complex point sets and the real point sets respectively, and put a bar to denote the orbit space for the involution of the complex conjugation, conj, for example, CX, RX, X = CX ..."

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1.1. A Rokhlin Conjecture and its variations. Considering real algebraic varieties, I use prefixes C and R to denote their complex point sets and the real point sets respectively, and put a bar to denote the orbit space for the involution of the complex conjugation, conj, for example, CX, RX, X = CX / conj. I identify

### QUOTIENTS BY COMPLEX CONJUGATION FOR REAL COMPLETE INTERSECTION SURFACES

, 1995

"... Abstract. Quotients Y = X/conj by the complex conjugation conj: X → X for complex surfaces X defined over R tend to be completely decomposable when they are simply connected, i.e., split into connected sums #nCP 2 #mCP 2 if w2(Y) ̸ = 0, or into #n(S 2 ×S 2) if w2(Y) = 0. The author proves this prop ..."

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Abstract. Quotients Y = X/conj by the complex conjugation conj: X → X for complex surfaces X defined over R tend to be completely decomposable when they are simply connected, i.e., split into connected sums #nCP 2 #mCP 2 if w2(Y) ̸ = 0, or into #n(S 2 ×S 2) if w2(Y) = 0. The author proves this property for complete intersections which are constructed by method of a small perturbation. We mean by a Real variety (Real curve, Real surface etc.) a pair (X, conj), where X is a complex variety and conj: X → X an anti-holomorphic involution called the real structure or the complex conjugation. Given an algebraic variety over R we consider the set of its complex points with the natural