Steenrod Connections and Connectivity in $H$-Spaces
| Author | : James P. Lin |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 98 |
| Release | : 1987 |
| Genre | : Mathematics |
| ISBN | : 0821824317 |
Steenrod Connections And Connectivity In H Spaces
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Encyclopaedia of Mathematics
| Author | : Michiel Hazewinkel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 743 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 9400903650 |
This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Geometric topology
| Author | : William Hilal Kazez |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 622 |
| Release | : 1996-10-22 |
| Genre | : Mathematics |
| ISBN | : 9780821806548 |
This is Part 1 of a two-part volume reflecting the proceedings of the 1993 Georgia International Topology Conference held at the University of Georgia during the month of August. The texts include research and expository articles and problem sets. The conference covered a wide variety of topics in geometric topology. Features: Kirby's problem list, which contains a thorough description of the progress made on each of the problems and includes a very complete bibliography, makes the work useful for specialists and non-specialists who want to learn about the progress made in many areas of topology. This list may serve as a reference work for decades to come. Gabai's problem list, which focuses on foliations and laminations of 3-manifolds, collects for the first time in one paper definitions, results, and problems that may serve as a defining source in the subject area.
Spectra and the Steenrod Algebra
| Author | : H.R. Margolis |
| Publisher | : Elsevier |
| Total Pages | : 511 |
| Release | : 2011-08-18 |
| Genre | : Mathematics |
| ISBN | : 0080960170 |
I have intended this book to be more than just the sum of its chapters, and the introduction is, in part, an attempt to spell out what the more is. Algebraic topology is the study of topological problems by algebraic means. More precisely, this has come to be framed as the study of topological categories by means of functors to algebraic categories. Beyond the basic definitions and structure, the focus is often on particular problems, for example, Adams’ use of K-theory to solve the vector fields on spheres problem. On the other hand, there are contributions of a more global nature yielding insight into the overall structure of some topological category, for example, Quillen’s work on rational homotopy type. This book is intended primarily as a contribution of this latter sort. So while there will be a variety of particular examples and computations, and although the structure being developed has significant application to many specific problems (some of which are considered here), the major thrust of the text is toward understanding the global structure and linkage of the topological and algebraic categories considered: the stable homotopy category and the category of modules over the Steenrod algebra.
Stable Homotopy Around the Arf-Kervaire Invariant
| Author | : Victor P. Snaith |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 250 |
| Release | : 2009-03-28 |
| Genre | : Mathematics |
| ISBN | : 376439904X |
Were I to take an iron gun, And ?re it o? towards the sun; I grant ‘twould reach its mark at last, But not till many years had passed. But should that bullet change its force, And to the planets take its course, ‘Twould never reach the nearest star, Because it is so very far. from FACTS by Lewis Carroll [55] Let me begin by describing the two purposes which prompted me to write this monograph. This is a book about algebraic topology and more especially about homotopy theory. Since the inception of algebraic topology [217] the study of homotopy classes of continuous maps between spheres has enjoyed a very exc- n n tional, central role. As is well known, for homotopy classes of maps f : S ?? S with n? 1 the sole homotopy invariant is the degree, which characterises the homotopy class completely. The search for a continuous map between spheres of di?erent dimensions and not homotopic to the constant map had to wait for its resolution until the remarkable paper of Heinz Hopf [111]. In retrospect, ?nding 3 an example was rather easy because there is a canonical quotient map from S to 3 1 1 2 theorbitspaceofthe freecircleactionS /S =CP = S .
Connections, Curvature, and Cohomology Volume 3
| Author | : Werner Greub |
| Publisher | : Academic Press |
| Total Pages | : 617 |
| Release | : 1976-02-19 |
| Genre | : Mathematics |
| ISBN | : 0080879276 |
Connections, Curvature, and Cohomology Volume 3
Algebraic Topology and Algebraic K-Theory (AM-113), Volume 113
| Author | : William Browder |
| Publisher | : Princeton University Press |
| Total Pages | : 567 |
| Release | : 2016-03-02 |
| Genre | : Mathematics |
| ISBN | : 1400882117 |
This book contains accounts of talks held at a symposium in honor of John C. Moore in October 1983 at Princeton University, The work includes papers in classical homotopy theory, homological algebra, rational homotopy theory, algebraic K-theory of spaces, and other subjects.
Classifying Spaces for Surgery and Corbordism of Manifolds. (AM-92), Volume 92
| Author | : Ib Madsen |
| Publisher | : Princeton University Press |
| Total Pages | : 296 |
| Release | : 2016-03-02 |
| Genre | : Mathematics |
| ISBN | : 1400881471 |
Beginning with a general discussion of bordism, Professors Madsen and Milgram present the homotopy theory of the surgery classifying spaces and the classifying spaces for the various required bundle theories. The next part covers more recent work on the maps between these spaces and the properties of the PL and Top characteristic classes, and includes integrality theorems for topological and PL manifolds. Later chapters treat the integral cohomology of BPL and Btop. The authors conclude with a discussion of the PL and topological cobordism rings and a construction of the torsion-free generators.
Connections, Curvature, and Cohomology
| Author | : Werner Hildbert Greub |
| Publisher | : Academic Press |
| Total Pages | : 618 |
| Release | : 1972 |
| Genre | : Mathematics |
| ISBN | : 0123027039 |
This monograph developed out of the Abendseminar of 1958-1959 at the University of Zürich. The purpose of this monograph is to develop the de Rham cohomology theory, and to apply it to obtain topological invariants of smooth manifolds and fibre bundles. It also addresses the purely algebraic theory of the operation of a Lie algebra in a graded differential algebra.
Cohomology of Finite Groups
| Author | : Alejandro Adem |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 329 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 3662062801 |
Some Historical Background This book deals with the cohomology of groups, particularly finite ones. Historically, the subject has been one of significant interaction between algebra and topology and has directly led to the creation of such important areas of mathematics as homo logical algebra and algebraic K-theory. It arose primarily in the 1920's and 1930's independently in number theory and topology. In topology the main focus was on the work ofH. Hopf, but B. Eckmann, S. Eilenberg, and S. MacLane (among others) made significant contributions. The main thrust of the early work here was to try to understand the meanings of the low dimensional homology groups of a space X. For example, if the universal cover of X was three connected, it was known that H2(X; A. ) depends only on the fundamental group of X. Group cohomology initially appeared to explain this dependence. In number theory, group cohomology arose as a natural device for describing the main theorems of class field theory and, in particular, for describing and analyzing the Brauer group of a field. It also arose naturally in the study of group extensions, N
