5,808 research outputs found
Algorithmic aspects of branched coverings
This is the announcement, and the long summary, of a series of articles on
the algorithmic study of Thurston maps. We describe branched coverings of the
sphere in terms of group-theoretical objects called bisets, and develop a
theory of decompositions of bisets.
We introduce a canonical "Levy" decomposition of an arbitrary Thurston map
into homeomorphisms, metrically-expanding maps and maps doubly covered by torus
endomorphisms. The homeomorphisms decompose themselves into finite-order and
pseudo-Anosov maps, and the expanding maps decompose themselves into rational
maps.
As an outcome, we prove that it is decidable when two Thurston maps are
equivalent. We also show that the decompositions above are computable, both in
theory and in practice.Comment: 60-page announcement of 5-part text, to apper in Ann. Fac. Sci.
Toulouse. Minor typos corrected, and major rewrite of section 7.8, which was
studying a different map than claime
On the Equivalence of Geometric and Analytic K-Homology
We give a proof that the geometric K-homology theory for finite CW-complexes
defined by Baum and Douglas is isomorphic to Kasparov's K-homology. The proof
is a simplification of more elaborate arguments which deal with the geometric
formulation of equivariant K-homology theory.Comment: 29 pages, v4: corrected definition of E in proof of Prop 3.
Regulators and cycle maps in higher-dimensional differential algebraic K-theory
We develop differential algebraic K-theory of regular arithmetic schemes. Our
approach is based on a new construction of a functorial, spectrum level
Beilinson regulator using differential forms. We construct a cycle map which
represents differential algebraic K-theory classes by geometric vector bundles.
As an application we derive Lott's relation between short exact sequences of
geometric bundles with a higher analytic torsion form.Comment: 106 pages (corrects a mistake in the sheaf condition), published
versio
The Development of Intersection Homology Theory
This historical introduction is in two parts. The first is reprinted with
permission from ``A century of mathematics in America, Part II,'' Hist. Math.,
2, Amer. Math. Soc., 1989, pp.543-585. Virtually no change has been made to the
original text. In particular, Section 8 is followed by the original list of
references. However, the text has been supplemented by a series of endnotes,
collected in the new Section 9 and followed by a second list of references. If
a citation is made to the first list, then its reference number is simply
enclosed in brackets -- for example, [36]. However, if a citation is made to
the second list, then its number is followed by an `S' -- for example, [36S].
Further, if a subject in the reprint is elaborated on in an endnote, then the
subject is flagged in the margin by the number of the corresponding endnote,
and the endnote includes in its heading, between parentheses, the page number
or numbers on which the subject appears in the reprint below. Finally, all
cross-references appear as hypertext links in the dvi and pdf copies.Comment: 58 pages, hypertext links added; appeared in Part 3 of the special
issue of Pure and Applied Mathematics Quarterly in honor of Robert
MacPherson. However, the flags in the margin were unfortunately (and
inexplicably) omitted from the published versio
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