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Foundational Essays on Topological Manifolds, Smoothings, and Triangulations.
Robion Kirby,L. C. Siebenmann +1 more
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TLDR
The first connected account of Kirby's and Siebenmann's basic research in this area is given in this article, followed by three articles by the authors that initially appeared between 1968 and 1970.Abstract:
Since Poincare's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area. The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.read more
Citations
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Journal ArticleDOI
Topological field theory
Book ChapterDOI
Algebraic K-theory of spaces
TL;DR: The algebraic K-theory of spaces as mentioned in this paper is a variant of the standard algebraic ktheory for topology, introduced by F. Waldhausen in the late 1970s.
Book
The geometry and topology of Coxeter groups
TL;DR: The authors introduced the theory of Coxeter groups in the context of the Lectures on Modern Mathematics Series at the Mathematical Sciences Center in Tsinghua University on May 10, 2013.
MonographDOI
Torus Actions and their Applications in Topology and Combinatorics
TL;DR: Polytopes topology and combinatorics of simplicial complexes Commutative and homological algebra of Cubical complexes Cubical Complexes Toric and quasitoric manifolds Moment-angle Complexes Cohomology of moment-angle complexes as discussed by the authors.
Journal ArticleDOI
Handlebody construction of Stein surfaces
TL;DR: In this article, the topology of Stein surfaces and contact 3-manifolds is studied by means of handle decompositions, which correspond to open handlebodies with all handles of index < 2.
References
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Book
Topology from the differentiable viewpoint
TL;DR: The fundamental theorem of algebra and its application to smooth manifolds and smooth maps was proved by Sard and Brown as discussed by the authors, and the Brouwer degree modulo 2 of a mapping was shown to be equivalent to the Hopf theorem.
Book
Analysis on Real and Complex Manifolds
TL;DR: In this article, the authors introduce the concept of linear elliptic operators with C Coefficients and apply it to open Riemann Surfaces, and show that it can be used to obtain the Frobenius Theorem, Hartog Continuation Theorem and Oka-Weil Theorem.