Except for a few added comments, this is a faithful translation of the book Strutture simpliciali in topologia, published by Pitagora Editrice, Bologna 2009, as part of the collection Quaderni of the Italian Mathematical Union. It should be noted that this book is neither a comprehensive text in algebraic topology nor is it a monograph on simplicial objects in the modern sense. Its focus is instead on the role of finite simplicial structures, and the algebraic topology deriving from them.
Topics in topology: The signature theorem and some of its applications
The author discusses several exciting topological developments that took place during the fifties decade which radically changed the way we think about many issues. Topics covered: Poincare duality, Thom isomorphism, Euler, Chern and Pontryagin classes, cobordisms groups, signature formula.
Added by: honhungoc | Karma: 8660.27 | Black Hole | 7 October 2010
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Curious and Interesting Geometry
A companion volume to the author's "Dictionary of Curious and Interesting Numbers", which focuses on arithmetic and number theory. The entries in this book cover curves, topology, tilings and all branches of plane and three-dimensional geometry, from Euclid to fractals.
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An introductory course in differential geometry and the Atiyah-Singer index theorem
This is a lecture-based class on the celebrated Atiyah-Singer index theorem, proved in the 60's by Sir Michael Atiyah and Isadore Singer. Their work on this theorem lead to a joint Abel prize in 2004. Requirements: Knowledge of topology and manifolds.
This book was written to be a readable introduction to Algebraic Topology with rather broad coverage of the subject. Our viewpoint is quite classical in spirit, and stays largely within the confines of pure Algebraic Topology. In a sense, the book could have been written thirty years ago since virtually all its content is at least thatold. However, the passage of the intervening years has helped clarify what the most important results and techniques are.
