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Covers the basic geometry of two and three-dimensional spaces. This work includes experiments to determine the true shape of the universe and contains illustrated examples and exercises that teach mind-expanding ideas. It explains how radiation remaining from the big bang may reveal the actual shape of the universe.
The theory of characteristic classes provides a meeting ground for the various disciplines of differential topology, differential and algebraic geometry, cohomology, and fiber bundle theory. As such, it is a fundamental and an essential tool in the study of differentiable manifolds. In this volume, the authors provide a thorough introduction...