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Lectures On Algebraic Topology
Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and student-friendly, but precise. Every lecture is accompanied by exercises. It begins slowly in order to gather up students with a variety of backgrounds, but gains pace as the course progresses, and by the end the student has a command of all the basic techniques of classical homotopy theory.
Handbook of Homotopy Theory
The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.
How the World Changed Social Media
How the World Changed Social Media is the first book in Why We Post, a book series that investigates the findings of anthropologists who each spent 15 months living in communities across the world. This book offers a comparative analysis summarising the results of the research and explores the impact of social media on politics and gender, education and commerce. What is the result of the increased emphasis on visual communication? Are we becoming more individual or more social? Why is public social media so conservative? Why does equality online fail to shift inequality offline? How did memes become the moral police of the internet? Supported by an introduction to the project’s academic framework and theoretical terms that help to account for the findings, the book argues that the only way to appreciate and understand something as intimate and ubiquitous as social media is to be immersed in the lives of the people who post. Only then can we discover how people all around the world have already transformed social media in such unexpected ways and assess the consequences
The Global Smartphone
The smartphone is often literally right in front of our nose, so you would think we would know what it is. But do we? To find out, 11 anthropologists each spent 16 months living in communities in Africa, Asia, Europe and South America, focusing on the take up of smartphones by older people. Their research reveals that smartphones are technology for everyone, not just for the young. The Global Smartphone presents a series of original perspectives deriving from this global and comparative research project. Smartphones have become as much a place within which we live as a device we use to provide ‘perpetual opportunism’, as they are always with us. The authors show how the smartphone is mor...
The Children of Jocasta
“[A] dark, elegant novel” of two women in ancient Greece, based on the great tragedies of Sophocles (Publishers Weekly). Thebes is a city in mourning, still reeling from a devastating plague that invaded every home and left the survivors devastated and fearful. This is the Thebes that Jocasta has known her entire life, a city ruled by a king—her husband-to-be. Jocasta struggles through this miserable marriage until she is unexpectedly widowed. Now free to choose her next husband, she selects the handsome, youthful Oedipus. When whispers emerge of an unbearable scandal, the very society that once lent Jocasta its support seems determined to destroy her. Ismene is a girl in mourning, lon...
The Ancient Guide to Modern Life
It's time for us to re-examine the past. Our lives are infinitely richer if we take the time to look at what the Greeks and Romans have given us in politics and law, religion and philosophy and education, and to learn how people really lived in Athens, Rome, Sparta and Alexandria. This is a book with a serious point to make but the author isn't simply a classicist but a comedian and broadcaster who has made television and radio documentaries about humour, education and Dorothy Parker. This is a book for us all. Whether political, cultural or social, there are endless parallels between the ancient and modern worlds. Whether it's the murder of Caesar or the political assassination of Thatcher; the narrative arc of the hit HBO series The Wire or that of Oedipus; the popular enthusiasm for the Emperor Titus or President Obama - over and over again we can be seen to be living very much like people did 2,000 or more years ago.
Algebraic Topology
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The Adams Spectral Sequence for Topological Modular Forms
The connective topological modular forms spectrum, $tmf$, is in a sense initial among elliptic spectra, and as such is an important link between the homotopy groups of spheres and modular forms. A primary goal of this volume is to give a complete account, with full proofs, of the homotopy of $tmf$ and several $tmf$-module spectra by means of the classical Adams spectral sequence, thus verifying, correcting, and extending existing approaches. In the process, folklore results are made precise and generalized. Anderson and Brown-Comenetz duality, and the corresponding dualities in homotopy groups, are carefully proved. The volume also includes an account of the homotopy groups of spheres throug...
Topological Modular Forms
The theory of topological modular forms is an intricate blend of classical algebraic modular forms and stable homotopy groups of spheres. The construction of this theory combines an algebro-geometric perspective on elliptic curves over finite fields with techniques from algebraic topology, particularly stable homotopy theory. It has applications to and connections with manifold topology, number theory, and string theory. This book provides a careful, accessible introduction to topological modular forms. After a brief history and an extended overview of the subject, the book proper commences with an exposition of classical aspects of elliptic cohomology, including background material on ellip...
On Thom Spectra, Orientability, and Cobordism
Rudyak’s groundbreaking monograph is the first guide on the subject of cobordism since Stong's influential notes of a generation ago. It concentrates on Thom spaces (spectra), orientability theory and (co)bordism theory (including (co)bordism with singularities and, in particular, Morava K-theories). These are all framed by (co)homology theories and spectra. The author has also performed a service to the history of science in this book, giving detailed attributions.
