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A Concise Course in Algebraic Topology
Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.
Towards Higher Categories
The purpose of this book is to give background for those who would like to delve into some higher category theory. It is not a primer on higher category theory itself. It begins with a paper by John Baez and Michael Shulman which explores informally, by analogy and direct connection, how cohomology and other tools of algebraic topology are seen through the eyes of n-category theory. The idea is to give some of the motivations behind this subject. There are then two survey articles, by Julie Bergner and Simona Paoli, about (infinity,1) categories and about the algebraic modelling of homotopy n-types. These are areas that are particularly well understood, and where a fully integrated theory ex...
More Concise Algebraic Topology
With firm foundations dating only from the 1950s, algebraic topology is a relatively young area of mathematics. There are very few textbooks that treat fundamental topics beyond a first course, and many topics now essential to the field are not treated in any textbook. J. Peter May’s A Concise Course in Algebraic Topology addresses the standard first course material, such as fundamental groups, covering spaces, the basics of homotopy theory, and homology and cohomology. In this sequel, May and his coauthor, Kathleen Ponto, cover topics that are essential for algebraic topologists and others interested in algebraic topology, but that are not treated in standard texts. They focus on the loca...
Simplicial Objects in Algebraic Topology
Simplicial sets are discrete analogs of topological spaces. They have played a central role in algebraic topology ever since their introduction in the late 1940s, and they also play an important role in other areas such as geometric topology and algebraic geometry. On a formal level, the homotopy theory of simplicial sets is equivalent to the homotopy theory of topological spaces. In view of this equivalence, one can apply discrete, algebraic techniques to perform basic topological constructions. These techniques are particularly appropriate in the theory of localization and completion of topological spaces, which was developed in the early 1970s. Since it was first published in 1967, Simpli...
Equivariant Stable Homotopy Theory
This book is a foundational piece of work in stable homotopy theory and in the theory of transformation groups. It may be roughly divided into two parts. The first part deals with foundations of (equivariant) stable homotopy theory. A workable category of CW-spectra is developed. The foundations are such that an action of a compact Lie group is considered throughout, and spectra allow desuspension by arbitrary representations. But even if the reader forgets about group actions, he will find many details of the theory worked out for the first time. More subtle constructions like smash products, function spectra, change of group isomorphisms, fixed point and orbit spectra are treated. While it is impossible to survey properly the material which is covered in the book, it does boast these general features: (i) a thorough and reliable presentation of the foundations of the theory; (ii) a large number of basic results, principal applications, and fundamental techniques presented for the first time in a coherent theory, unifying numerous treatments of special cases in the literature.
Runaway
"MAY IS GOING FROM STRENGTH TO STRENGTH... A WONDERFUL EXHIBITION OF JUST HOW GOOD MAY CAN BE." --The Daily Mail "Five of us had run away that fateful night just over a month before. Only three of us would be going home. And nothing, nothing would ever be the same again." Glasgow, 1965. Headstrong teenager Jack Mackay has just one destination on his mind--London--and successfully convinces his four friends, and fellow bandmates, to join him in abandoning their homes to pursue a goal of musical stardom. Glasgow, 2015. Jack Mackay, heavy-hearted sixty-seven-year-old is still haunted by what might have been. His recollections of the terrible events that befell him and his friends some fifty years earlier, and how he did not act when it mattered most is a memory he has tried to escape his entire adult life. London, 2015. A man lies dead in a one-room flat. His killer looks on, remorseless. What started with five teenagers following a dream five decades before has been transformed over the intervening decades into a waking nightmare that might just consume them all.
Equivariant Homotopy and Cohomology Theory
This volume introduces equivariant homotopy, homology, and cohomology theory, along with various related topics in modern algebraic topology. It explains the main ideas behind some of the most striking recent advances in the subject. The works begins with a development of the equivariant algebraic topology of spaces culminating in a discussion of the Sullivan conjecture that emphasizes its relationship with classical Smith theory. The book then introduces equivariant stable homotopy theory, the equivariant stable homotopy category, and the most important examples of equivariant cohomology theories. The basic machinery that is needed to make serious use of equivariant stable homotopy theory is presented next, along with discussions of the Segal conjecture and generalized Tate cohomology. Finally, the book gives an introduction to "brave new algebra", the study of point-set level algebraic structures on spectra and its equivariant applications. Emphasis is placed on equivariant complex cobordism, and related results on that topic are presented in detail.
The Selected Works of J. Frank Adams
The selected works of one the greatest names in algebraic topology.
The Blackhouse
THE 12 MILLION COPY BESTSELLING AUTHOR OF THE ENZO FILES AND THE CHINA THRILLERS AWARD WINNING AUTHOR OF THE CWA DAGGER IN THE LIBRARY 2021 'One of the best regarded crime series of recent years.' Independent 'No one can create a more eloquently written suspense novel than Peter May.' New York Journal of Books PETER MAY: THE MAN WHO BROUGHT MURDER TO THE OUTER HEBRIDES A brutal killing takes place on the Isle of Lewis, Scotland: a land of harsh beauty and inhabitants of deep-rooted faith. A MURDER Detective Inspector Fin Macleod is sent from Edinburgh to investigate. For Lewis-born Macleod, the case represents a journey both home and into his past. A SECRET Something lurks within the close-knit island community. Something sinister. A TRAP As Fin investigates, old skeletons begin to surface, and soon he, the hunter, becomes the hunted. LOVED THE BLACKHOUSE? Read book 2 in the Lewis trilogy, THE LEWIS MAN LOVE PETER MAY? Buy his latest frontlist thriller, THE NIGHT GATE
