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Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88
Since Poincaré'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 Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.
Acne
Emphasis is place on the knowledge of the disease, its investigation and its treatment. Invaluable for the training dermatologists and physicians completing their specialist training.
The Hauptvermutung Book
The Hauptvermutung is the conjecture that any two triangulations of a poly hedron are combinatorially equivalent. The conjecture was formulated at the turn of the century, and until its resolution was a central problem of topology. Initially, it was verified for low-dimensional polyhedra, and it might have been expected that furt her development of high-dimensional topology would lead to a verification in all dimensions. However, in 1961 Milnor constructed high-dimensional polyhedra with combinatorially inequivalent triangulations, disproving the Hauptvermutung in general. These polyhedra were not manifolds, leaving open the Hauptvermu tung for manifolds. The development of surgery theory le...
Induction Theorems for Groups of Homotopy Manifold Structures
Classifying spaces in surgery theory were first used by Sullivan and Casson in their (independent) unpublished work on the Hauptvermutung for PL manifolds. In his 1968 Ph.D. thesis, F. Quinn developed a general theory of surgery classifying spaces, realizing the Wall surgery groups as the homotopy groups [italic]L[subscript]*([italic]G) = [lowercase Greek]Pi[subscript]*([italic]L([italic]G)) of a spectrum of manifold n-ad surgery problems with fundamental group G. This work presents a detailed account of Quinn's theory. Geometric methods are used to view the Sullivan-Wall manifold structure sequence as an exact sequence of abelian groups (as suggested by Quinn). The intersection of the known induction theorems for generalized cohomology groups and [italic]L-groups then gives an induction theorem for the structure sequence with finite [italic]G.
Rook's Textbook of Dermatology
The late Arthur Rook established the Textbook of Dermatologyas the most comprehensive work of reference available to thedermatologist and it enjoys instant name recognition. Eachsubsequent edition has been expanded as the subject has developedand the book remains the ultimate source of clinical informationfor the trainee and practising dermatologist alike. Rook's Textbook of Dermatology covers all aspects of skindisease from basic science through pathology and epidemiology toclinical practice. Long recognized for its unparalleled coverage ofdiagnosis, this clinical classic earned its reputation as adefinitive source of information. New features of this Seventh Edition include: Two new Editors, Neil Cox and Christopher Griffiths, join theteam Every chapter is updated and several are completely rewrittenfrom scratch Completely new chapter on AIDS and the Skin Traditional emphasis on diagnosis preserved More coverage of treatment in each of the disease-specificchapters
Surfaces in 4-Space
Surfaces in 4-Space, written by leading specialists in the field, discusses knotted surfaces in 4-dimensional space and surveys many of the known results in the area. Results on knotted surface diagrams, constructions of knotted surfaces, classically defined invariants, and new invariants defined via quandle homology theory are presented. The last chapter comprises many recent results, and techniques for computation are presented. New tables of quandles with a few elements and the homology groups thereof are included. This book contains many new illustrations of knotted surface diagrams. The reader of the book will become intimately aware of the subtleties in going from the classical case of knotted circles in 3-space to this higher dimensional case. As a survey, the book is a guide book to the extensive literature on knotted surfaces and will become a useful reference for graduate students and researchers in mathematics and physics.
Algebraic and Geometric Topology, Part 2
Contains sections on Structure of topological manifolds, Low dimensional manifolds, Geometry of differential manifolds and algebraic varieties, $H$-spaces, loop spaces and $CW$ complexes, Problems.
Classgroups of Group Rings
This book is a self-contained account of the theory of classgroups of group rings. The guiding philosophy has been to describe all the basic properties of such classgroups in terms of character functions. This point of view is due to A. Frohlich and it achieves a considerable simplification and clarity over previous techniques. A main feature of the book is the introduction of the author's group logarithm, with numerous examples of its application. The main results dealt with are: Ullom's conjecture for Swan modules of p-groups; the self-duality theorem for rings of integers of tame extensions; the fixed-point theorem for determinants of group rings; the existence of Adams operations on classgroups. In addition, the author includes a number of calculations of classgroups of specific families of groups such as generalized dihedral groups, and quaternion and dihedral 2-groups. The work contained in this book should be readily accessible to any graduate student in pure mathematics who has taken a course in the representation theory of finite groups. It will also be of interest to number theorists and algebraic topologists.
Geometric Aspects of General Topology
This book is designed for graduate students to acquire knowledge of dimension theory, ANR theory (theory of retracts), and related topics. These two theories are connected with various fields in geometric topology and in general topology as well. Hence, for students who wish to research subjects in general and geometric topology, understanding these theories will be valuable. Many proofs are illustrated by figures or diagrams, making it easier to understand the ideas of those proofs. Although exercises as such are not included, some results are given with only a sketch of their proofs. Completing the proofs in detail provides good exercise and training for graduate students and will be usefu...
Introduction to Combinatorial Torsions
This book is an introduction to combinatorial torsions of cellular spaces and manifolds with special emphasis on torsions of 3-dimensional manifolds. The first two chapters cover algebraic foundations of the theory of torsions and various topological constructions of torsions due to K. Reidemeister, J.H.C. Whitehead, J. Milnor and the author. We also discuss connections between the torsions and the Alexander polynomials of links and 3-manifolds. The third (and last) chapter of the book deals with so-called refined torsions and the related additional structures on manifolds, specifically homological orientations and Euler structures. As an application, we give a construction of the multivaria...
