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PERCOLATION ON THE PROJECTIVE PLANE
 MATHEMATICAL RESEARCH LETTERS 4, 889–894 (1997)
, 1997
"... Since the projective plane is closed, the natural homological observable ofa percolation process is the presence ofthe essential cycle in H1(RP 2; Z2). In the Voroni model at critical phase, pc =.5, this observable has probability q =.5 independent ofthe metric on RP 2. This establishes a single ins ..."
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Cited by 8 (2 self)
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Since the projective plane is closed, the natural homological observable ofa percolation process is the presence ofthe essential cycle in H1(RP 2; Z2). In the Voroni model at critical phase, pc =.5, this observable has probability q =.5 independent ofthe metric on RP 2. This establishes a single instance (RP 2, homological observable) ofa very general conjecture about the conformal invariance ofpercolation due to Aizenman and Langlands, for which there is much moral and numerical evidence but no previously verified instances. On RP 2 all metrics are conformally equivalent so the proof of metric independence is precisely what the conjecture would predict. What is very special, is that at pc metric invariance holds in all finite models so passing to the limit is trivial; the probability q is fixed at.5 by a topological symmetry.
Noncommutative Localization in Topology
, 2003
"... this paper deal with spaces (especially manifolds) with infinite fundamental group, and involve localizations of infinite group rings and related triangular matrix rings. Algebraists have usually considered noncommutative localization of rather better behaved rings, so the topological applications r ..."
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this paper deal with spaces (especially manifolds) with infinite fundamental group, and involve localizations of infinite group rings and related triangular matrix rings. Algebraists have usually considered noncommutative localization of rather better behaved rings, so the topological applications require new algebraic techniques
The bordism of automorphisms of manifolds from the algebraic Ltheory point of view
"... this paper the bordism of automorphisms of highdimensional manifolds is considered from the point of view of the localization exact sequence in algebraic Ltheory. ..."
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this paper the bordism of automorphisms of highdimensional manifolds is considered from the point of view of the localization exact sequence in algebraic Ltheory.
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 welldeveloped 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