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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.
These are proceedings of an International Conference on Algebraic
Topology, held 28 July through 1 August, 1986, at Arcata,
California. The conference served in part to mark the 25th
anniversary of the journal "Topology" and 60th birthday of Edgar H.
Brown. It preceded ICM 86 in Berkeley, and was conceived as a
successor to the Aarhus conferences of 1978 and 1982. Some thirty
papers are included in this volume, mostly at a research level.
Subjects include cyclic homology, H-spaces, transformation groups,
real and rational homotopy theory, acyclic manifolds, the homotopy
theory of classifying spaces, instantons and loop spaces, and
complex bordism.
During the Winter and spring of 1985 a Workshop in Algebraic
Topology was held at the University of Washington. The course notes
by Emmanuel Dror Farjoun and by Frederick R. Cohen contained in
this volume are carefully written graduate level expositions of
certain aspects of equivariant homotopy theory and classical
homotopy theory, respectively. M.E. Mahowald has included some of
the material from his further papers, represent a wide range of
contemporary homotopy theory: the Kervaire invariant, stable
splitting theorems, computer calculation of unstable homotopy
groups, and studies of L(n), Im J, and the symmetric groups.
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.
Edward Witten once said that Elliptic Cohomology was a piece of
21st Century Mathematics that happened to fall into the 20th
Century. He also likened our understanding of it to what we know of
the topography of an archipelago; the peaks are beautiful and
clearly connected to each other, but the exact connections are
buried, as yet invisible. This very active subject has connections
to algebraic topology, theoretical physics, number theory and
algebraic geometry, and all these connections are represented in
the sixteen papers in this volume. A variety of distinct
perspectives are offered, with topics including equivariant complex
elliptic cohomology, the physics of M-theory, the modular
characteristics of vertex operator algebras, and higher chromatic
analogues of elliptic cohomology. This is the first collection of
papers on elliptic cohomology in almost twenty years and gives a
broad picture of the state of the art in this important field of
mathematics.
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