Geometry & Topology

Topology is a branch of pure mathematics related to Geometry that describes mathematical spaces, in particular the properties that stem from a space’s shape. Topology originates in the early part of the twentieth century, but some isolated results can be traced back several centuries. Many of the shapes topologists deal with are incredibly strange, so much so that practically all everyday objects such as bowls and pets and trees make up a small minority. Topology developed as a field of study out of geometry and set theory, through analysis of concepts such as space, dimension, and transformation. In its most general setting, topology involves objects that are abstract sets of elements. To discuss properties such as continuity of functions between such abstract sets, some additional structure must be imposed on them.

Geometry & Topology provides a glimpse of many research topics in modern algebra, geometry and topology. It presents an array of topics that introduce the reader to key ideas in active areas in geometry and topology. Algebraic geometry and complex manifolds and geometrical aspects of mathematical physics, and relations with manifold topology. This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. The material is presented in a way that both graduate students and researchers should find accessible and enticing.