This book arose from courses taught by the authors, and is designed for both instructional and reference use during and after a first course in algebraic topology. It is a handbook for users who want to calculate, but whose main interests are in applications using the current literature, rather than in developing the theory. Typical areas of applications are differential geometry and theoretical physics. We start gently, with numerous pictures to illustrate the fundamental ideas and constructions in homotopy theory that are needed in later chapters. We show how to calculate homotopy groups, homology groups and cohomology rings of most of the major theories, exact homotopy sequences of fibrations, some important spectral sequences, and all the obstructions that we can compute from these. Our approach is to mix illustrative examples with those proofs that actually develop transferable calculational aids. We give extensive appendices with notes on background material, extensive tables of data, and a thorough index. Audience: Graduate students and professionals in mathematics and physics.
Chevalia is an enchanted island where ponies and horses rule, its magic powered by eight golden horseshoes hanging in the royal castle-thanks to Pippa and Princess Stardust's efforts to find them all. Her task complete, Pippa has returned to our world . . . but her friends in Chevalia are never far away.
In A Special Surprise, Princess Stardust has come all the way from Chevalia to cheer Pippa on in her first big competition. But when Pippa arrives at the stables, her riding school pony friends are nowhere to be found. Stardust has an idea who is responsible . . . but for the show to go on, Pippa and Stardust must return to Chevalia! Offering a brand new mystery and black and white illustrations throughout, this winning combination of princesses, ponies and collectible jewelry is sure to enchant readers.