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A course on manifolds differs from most other introductory mathematics graduate courses in that the subject matter is often completely unfamiliar. Unlike algebra and analysis, which all math majors see as undergraduates, manifolds enter the curriculum much later. It is even possible to get through an entire undergraduate mathematics education without ever hearing the word "manifold." Yet manifolds are part of the basic vocabulary of modern mathematics, and students need to know them as intimately as they know the integers, the real numbers, Euclidean spaces, groups, rings, and fields.
In his beautifully-conceived Introduction, the author motivates the technical developments to follow by explaining some of the roles manifolds play in diverse branches of mathematics and physics. Then he goes on to introduce the basics of general topology and continues with the fundamental group, covering spaces, and elementary homology theory. Manifolds are introduced early and used as the main examples throughout.
John M. Lee is currently Professor of Mathematics at the University of Washington in Seattle. In addition to pursuing research in differential geometry and partial differential equations, he has been teaching undergraduate and graduate courses on manifolds at U.W. and Harvard University for more than fifteen years.
Hodge Theory of Projective Manifolds Автор: M Andrea De Cataldo Год: 2007 |
Manifolds with Cusps of Rank One: Spectral Theory and L2-lndex Theorem Автор: Werner Muller Год: 1987 |
Introduction to Manifolds Автор: Loring W. Tu Год: 2007 |
Manifolds with Cusps of Rank One Автор: Werner Müller Год: 1987 |
Symplectic geometry of integrable Hamiltonian systems Автор: Audin M., da Silva A.C., Lerman E. Год: 2003 |
Manifolds of nonpositive curvature Автор: Ballmann W., Gromov M., Schroeder V. Год: 1985 |