Topology

This textbook demonstrates how differential calculus, smooth manifolds, and commutative algebra constitute a unified whole, despite having arisen at different times and under different circumstances.

This book comprehensively examines various significant aspects of linear time-invariant systems theory, both for continuous-time and discrete-time.

This book gathers the proceedings of the 2018 Abel Symposium, which was held in Geiranger, Norway, on June 4-8, 2018.

This book offers a concise introduction to ergodic methods in group homology, with a particular focus on the computation of L2-Betti numbers.

These are notes from a graduate student course on algebraic topology and K-theory given by Daniel Quillen at the Massachusetts Institute of Technology during 1979-1980.

This book gives a systematic presentation of real algebraic varieties.

This collection of peer-reviewed workshop papers provides comprehensive coverage of cutting-edge research into topological approaches to data analysis and visualization.

This volume highlights the mathematical research presented at the 2019 Association for Women in Mathematics (AWM) Research Symposium held at Rice University, April 6-7, 2019.

This textbook offers readers a self-contained introduction to quantitative Tamarkin category theory.

The first monograph on singularities of mappings for many years, this book provides an introduction to the subject and an account of recent developments concerning the local structure of complex analytic mappings.

The primary aim of this monograph is to achieve part of Beilinson's program on mixed motives using Voevodsky's theories of A1-homotopy and motivic complexes.

This book is an exposition of the theoretical foundations of hyperbolic manifolds.

This book introduces the reader to the most important concepts and problems in the field of l2-invariants.

This book is an outcome of two Conferences on Ulam Type Stability (CUTS) organized in 2016 (July 4-9, Cluj-Napoca, Romania) and in 2018 (October 8-13, 2018, Timisoara, Romania).

This book aims to provide a friendly introduction to non-commutative geometry.

This textbook provides a gentle introduction to intersection homology and perverse sheaves, where concrete examples and geometric applications motivate concepts throughout.

This monograph could be used for a graduate course on symplectic geometry as well as for independent study.

This monograph initiates a theory of new categorical structures that generalize the simplicial Segal property to higher dimensions.

Developed over years of classroom use, this textbook provides a clear and accessible approach to real analysis.

Collecting together the lecture notes of the CIME Summer School held in Cetraro in July 2018, the aim of the book is to introduce a vast range of techniques which are useful in the investigation of complex manifolds.

This proceedings is based on the interdisciplinary workshop held in Madrid, 5-9 March 2018, dedicated to Alberto Ibort on his 60th birthday.

This book covers the fundamental results of the dimension theory of metrizable spaces, especially in the separable case.

This book addresses fixed point theory, a fascinating and far-reaching field with applications in several areas of mathematics.

This is an in-depth report on the endotrivial modules, an important class of modular representations for finite groups.

This book is the result of a meeting on Topology and Functional Analysis, and is dedicated to Professor Manuel Lopez-Pellicer's mathematical research.

This anthology aims to present the fundamental philosophical issues and tools required by the reflection within and upon geography and Geographic Information Systems (GIS) .

This book provides a generalised approach to fractal dimension theory from the standpoint of asymmetric topology by employing the concept of a fractal structure.

Graduate students and researchers in applied mathematics, optimization, engineering,  computer science, and  management science will find this book a useful reference which provides an introduction to applications and fundamental theories in nonlinear combinatorial optimization.

This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications.

This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research.

This monograph presents a new model of mathematical structures called weak n-categories.

This book provides an accessible introduction to knot theory, focussing on Vassiliev invariants, quantum knot invariants constructed via representations of quantum groups, and how these two apparently distinct theories come together through the Kontsevich invariant.

This is the first comprehensive monograph to thoroughly investigate constant width bodies, which is a classic area of interest within convex geometry.

In this partly expository work, a framework is developed for building exotic circle actions of certain classical groups.

This monograph presents a new model of mathematical structures called weak n-categories.

This anthology aims to present the fundamental philosophical issues and tools required by the reflection within and upon geography and Geographic Information Systems (GIS) .

A-infinity structure was introduced by Stasheff in the 1960s in his homotopy characterization of based loop space, which was the culmination of earlier works of Sugawara's homotopy characterization of H-spaces and loop spaces.

This invaluable book, based on the many years of teaching experience of both authors, introduces the reader to the basic ideas in differential topology.

This book is a written-up and expanded version of eight lectures on the Hodge theory of projective manifolds.

This book is aimed at the approximation of set-valued functions with compact sets in an Euclidean space as values.

Electrical, communication, transportation, computer, and neural networks are special kinds of nets.

Separate and Joint Continuity presents and summarises the main ideas and theorems that have been developed on this topic, which lies at the interface between General Topology and Functional Analysis (and the geometry of Banach spaces in particular).

GRE Formula Book is an excellent resource for students who are preparing to stand among the top scorers in GRE.

This monograph presents an approachable proof of Mirzakhani's curve counting theorem, both for simple and non-simple curves.

The theory of linear topological dynamics is a rapidly growing field of research over the last three decades or so.

The Only Undergraduate Textbook to Teach Both Classical and Virtual Knot TheoryAn Invitation to Knot Theory: Virtual and Classical gives advanced undergraduate students a gentle introduction to the field of virtual knot theory and mathematical research.

In knot theory, diagrams of a given canonical genus can be described by means of a finite number of patterns ("e;generators"e;).

The Only Undergraduate Textbook to Teach Both Classical and Virtual Knot TheoryAn Invitation to Knot Theory: Virtual and Classical gives advanced undergraduate students a gentle introduction to the field of virtual knot theory and mathematical research.

This book provides a comprehensive introduction to Submanifold theory, focusing on general properties of isometric and conformal immersions of Riemannian manifolds into space forms.

This volume provides a broad and uniform introduction of PDE-constrained optimization as well as to document a number of interesting and challenging applications.