Foundational Essays on Topological Manifolds, Smoothings, and Triangulations.

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 Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.

[1]  W. Blankinship,et al.  GENERALIZATION OF A CONSTRUCTION OF ANTOINE , 1951 .

[2]  M. Hirsch.  ON NORMAL MICROBUNDLES , 1966 .

[3]  D. Sullivan.  Geometric periodicity and the invariants of manifolds , 1971 .

[4]  L. E. Jones.  Patch Spaces: A Geometric Representation for Poincare Spaces , 1973 .

[5]  Level-preserving approximations and isotopies, and homotopy groups of spaces of embeddings , 1974 .

[6]  R. Kirby.  Stable homeomorphisms and the annulus conjecture , 1969 .

[7]  Chih-Han Sah,et al.  Symmetric bilinear forms and quadratic forms , 1972 .

[8]  B. Sanderson.  The simplicial extension theorem , 1975 .

[9]  M. Newman,et al.  The Engulfing Theorem for Topological Manifolds , 1966 .

[10]  H. Whitney.  The Self-Intersections of a Smooth n-Manifold in 2n-Space , 1944 .

[11]  L. Siebenmann.  Approximating cellular maps by homeomorphisms , 1972 .

[12]  C. Wall,et al.  On the homotopy type of compact topological manifolds , 1968 .

[13]  J. Cerf.  Groupes d'automorphismes et groupes de difféomorphismes des variétés compactes de dimension 3 , 1959 .

[14]  H. Toda.  Composition Methods in Homotopy Groups of Spheres , 1962 .

[15]  H. Whitney.  Analytic Extensions of Differentiable Functions Defined in Closed Sets , 1934 .

[16]  M. A. Armstrong.  FOUNDATIONAL ESSAYS ON TOPOLOGICAL MANIFOLDS, SMOOTHINGS AND TRIANGULATIONS , 1978 .

[17]  Jean-Pierre Serre.  Cours d'arithmétique , 1971 .

[18]  D. Mcmillan,et al.  Covering three-manifolds with open cells , 1969 .

[19]  J. Munkres.  Concordance is equivalent to smoothability , 1966 .

[20]  M. Hirsch.  On combinatorial submanifolds of differentiable manifolds , 1962 .

[21]  D. Anderson,et al.  Extending combinatorial PL structures on stratified spaces , 1976 .

[22]  J. Shaneson,et al.  Fake tori, the annulus conjecture, and the conjectures of kirby. , 1969, Proceedings of the National Academy of Sciences of the United States of America.

[23]  W. Browder.  Surgery on Simply-Connected Manifolds , 1972 .

[24]  M. Kervaire,et al.  Lectures on the theorem of Browder and Novikov and Siebenmann's thesis , 1969 .

[25]  T. Chapman,et al.  Topological Invariance of Whitehead Torsion , 1974 .

[26]  Wilfred Kaplan,et al.  Regular curve-families filling the plane, II , 1940 .

[27]  S. Lang.  Introduction to Differentiable Manifolds , 1964 .

[28]  R. Edwards.  The equivalence of close piecewise linear embeddings , 1975 .

[29]  Jean-Pierre Serre,et al.  Groupes d'homotopie et classes des groupes abeliens , 1953 .

[30]  R. T. Miller.  Mapping cylinder neighborhoods of some ANR's , 1976 .

[31]  J. Lees.  Immersions and surgeries of topological manifolds , 1969 .

[32]  D. Sullivan,et al.  The Transversality Characteristic Class and Linking Cycles in Surgery Theory , 1974 .

[33]  John Milnor,et al.  On spaces having the homotopy type of a CW-complex , 1959 .

[34]  W. Lickorish,et al.  Piecewise linear critical levels and collapsing , 1972 .

[35]  Bernard Malgrange,et al.  Ideals of differentiable functions , 1966 .

[36]  M. Scharlemann.  Constructing strange manifolds with the dodecahedral space , 1976 .

[37]  D. Puppe,et al.  Differenzierbare Strukturen auf Mannigfaltigkeiten ohne abzählbare Basis , 1968 .

[38]  R. Narasimhan,et al.  Analysis on Real and Complex Manifolds , 1973 .

[39]  F. Farrell.  The obstruction to fibering a manifold over a circle , 1967 .

[40]  J. Shaneson.  Wall's Surgery Obstruction Groups for G × Z , 1969 .

[41]  A. Dold.  Partitions of Unity in the Theory of Fibrations , 1963 .

[42]  L. Neuwirth.  A topological classification of certain 3-manifolds , 1963 .

[43]  J. Cerf.  La stratification naturelle des espaces de fonctions différentiables réelles et le théorème de la pseudo-isotopie , 1970 .

[44]  M. Hirsch.  On non-linear cell bundles , 1966 .

[45]  R. Kirby,et al.  Normal bundles for codimension 2 locally flat imbeddings , 1975 .

[46]  J. Milnor.  Topology from the differentiable viewpoint , 1965 .

[47]  Yukio Matsumoto,et al.  The unstable difference between homology cobordism and piecewise linear block bundles , 1975 .

[48]  J. Whitehead,et al.  Manifolds with Transverse Fields in Euclidean Space , 1961 .

[49]  G. Brumfiel.  The homotopy groups of $BPL$ and $PL/O$. III. , 1970 .

[50]  M. Hirsch,et al.  Surgery on piecewise linear manifolds and applications , 1966 .

[51]  E. Brown.  ABSTRACT HOMOTOPY THEORY , 1965 .

[52]  L. Siebenmann.  On detecting euclidean space homotopically among topological manifolds , 1968 .

[53]  THE CRITICAL POINTS OF A FUNCTION OF n VARIABLES. , 1930, Proceedings of the National Academy of Sciences of the United States of America.