Topology, Geometry, and Gauge Fields

1. Front Matter

   Pages i-xviii

   PDF

2. Physical and Geometrical Motivation

   • Gregory L. Naber

   Pages 1-26

3. Topological Spaces

   • Gregory L. Naber

   Pages 27-100

4. Homotopy Groups

   • Gregory L. Naber

   Pages 101-164

5. Principal Bundles

   • Gregory L. Naber

   Pages 165-184

6. Differentiable Manifolds and Matrix Lie Groups

   • Gregory L. Naber

   Pages 185-290

7. Gauge Fields and Instantons

   • Gregory L. Naber

   Pages 291-365

8. Back Matter

   Pages 367-396

   PDF

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas­ sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). The development ofnewcourses is a natural consequence of a high levelof excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied mathe­ matical Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. Preface In Egypt, geometry was created to measure the land. Similar motivations, on a somewhat larger scale, led Gauss to the intrinsic differential geometry of surfaces in space. Newton created the calculus to study the motion of physical objects (apples, planets, etc.) and Poincare was similarly impelled toward his deep and far-reaching topological view of dynamical systems.

• electromagnetic field
• fields
• gauge theory
• geometry
• mechanics
• physics
• quantum mechanics
• topology

• Department of Mathematics and Statistics, California State University, Chico, Chico, USA

  Gregory L. Naber

Policies and ethics