Group Theory Dinesh Khattar

Topological Methods in Group Theory is about the interplay between algebraic topology and the theory of infinite discrete groups. The author has kept three kinds of readers in mind: graduate students who have had an introductory course in algebraic topology and who need a bridge from common knowledge to the current research literature in geometric, combinatorial and homological group theory; group theorists who would like to know more about the topological side of their subject but who have been too long away from topology; and manifold topologists, both high- and low-dimensional, since the book contains much basic material on proper homotopy and locally finite homology not easily found elsewhere.

Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts. But its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective.

This textbook provides a didactic introduction to the topic of group theory in physics, with a special focus on solid state physics issues. The book is useful for students who encounter such problems in their first scientific work (in theory or experiment). In addition to the basic introduction to group theory and representation theory, the book deals with point groups, double point groups, and space groups, which are essential in solid state physics. As an example for systems with space group symmetry, electrons in periodic potentials are discussed.