Topology (1) (Photocopy) General Overview

Author: S.P. Novikov
Publisher:
Publication Date: 2006-01-17
Features: The author is one of the most renowned experts in the field of topology and has received the Fields Medal and the Wolf Prize in Mathematics. This book provides a new survey of the entire field of topology (excluding general topology (set-theoretic topology)). According to Novikov's own perspective, topology was called "analysis situs" in the late 19th century and later divided into different fields such as combinatorial topology, algebraic topology, differential topology, homotopy topology, and geometric topology. This book begins with the fundamental principles and then elaborates on the current research frontiers, summarizing these fields. Chapter 2 introduces fiber spaces; Chapter 3 discusses CW-complexes, homology and homotopy theory, duality theory, K-theory, and the Adams-Novikov spectral sequence; Chapter 4 comprehensively (and concisely) discusses manifold theory. The appendix roughly outlines the notable new developments in knot theory, linking theory, and low-dimensional topology. Through this book, readers can gain a comprehensive understanding of the concepts of topology. It serves as a guide and will encourage different authors to provide more detailed surveys of these fields of topology.