A Course on Surgery Theory: (AMS-211)
A Course on Surgery Theory: (AMS-211)
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Abstract
Surgery theory, a subfield of geometric topology, is the study of the classifications of manifolds. This book offers a modern look at this important mathematical discipline and some of its applications. The book explains some of the triumphs of surgery theory during the past three decades, from both an algebraic and geometric point of view. It also provides an extensive treatment of basic ideas, main theorems, active applications, and recent literature. The authors methodically cover all aspects of surgery theory, connecting it to other relevant areas of mathematics, including geometry, homotopy theory, analysis, and algebra. Later chapters are self-contained, so readers can study them directly based on topic interest. Of significant use to high-dimensional topologists and researchers in noncommutative geometry and algebraic K-theory, the book serves as an important resource for the mathematics community.
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Front Matter
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Introduction
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One
The characterization of homotopy types
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Two
Some calculations of L-groups
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Three
Classical surgery theory
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Four
Topological surgery and surgery spaces
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Five
Applications of the assembly map
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Six
Beyond characteristic classes
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Seven
Flat and almost flat manifolds
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Eight
Other surgery theories
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End Matter
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