Towards Higher Categories (The IMA Volumes in Mathematics and its Applications)
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.
Fundamentals of General Topology: Problems and Exercises
`This problem set is carefully designed; if the student goes through all the problems in the book then at the end he is familiar with almost all basic notions in general topology. In addition to this, he knows more what mathematics is about than can be expected of a student taking an ordinary course in general topology. This book is well written and will be of lasting importance to both teachers and students in general topology.' Zentralblatt für Mathematik, 568 (1986)
"A General Topology Workbook" presents elementary general topology in an unconventional way. Highly influenced by the legendary ideas of R.L. Moore, the author has taught several generations of mathematics students with these materials, proving again the usefulness and stimulation of the Moore method. The first part of the book gives a quick review of the basic definitions of the subject, interspersed with a large number of exercises, some of which are described as theorems.
Floer Homology, Gauge Theory, and Low Dimensional Topology
Mathematical gauge theory studies connections on principal bundles, or, more precisely, the solution spaces of certain partial differential equations for such connections. Historically, these equations have come from mathematical physics, and play an important role in the description of the electro-weak and strong nuclear forces.
The purpose of this text is to make familiar with the basics of topology, to give a concise introduction to homotopy, and to make students familiar with homology. Readers are expected to have successfully completed their first year courses in analysis and linear algebra.
