Topology – Mathematical Association of America

Featured Resources

From wandering to wayfinding: Moving Beyond Shiny Object Syndrome

By Lew Ludwig "The deep breath before the plunge" - a sentiment Gandalf shares with Pippin in the Return of the King. This phrase often runs through my mind as the last days of summer break wind down and the new school year is about to begin. To be clear, I do not see the new...

Complement (bottom-up) learning with top-down activities to develop mathematical thinking ability

By Keith Devlin @KeithDevlin@fediscience.org, @profkeithdevlin.bsky.social Sometime in the early 2000s, my primary care physician offered me the option of no longer having an annual health checkup in person. Rather, I could just call into my nearest walk-in testing lab and have a blood draw, followed up a few days later by a quick video-chat. (They also wanted...

Fixed Point Theory in Generalized Metric Spaces

Fixed point theory is one of the major research areas in nonlinear functional analysis, topologyand real analysis, which deals with the study of fixed points of functions. A fixed point of afunction is a point in the domain of the function that is mapped to itself by the function. Fixedpoint theory also has several applications...

Book cover of "Fixed Point Theory in Generalized Metric Spaces" by Erdal Karapinar and Ravi P. Agarwal. The background is a gradient of purple hues with white and black text. The series title, “Synthesis Lectures on Mathematics & Statistics,” appears at the top under a red and navy banner. The publisher logos for "Synthesis Collection of Technology" and "Springer" are displayed at the top and bottom respectively.

Symplectic and Contact Geometry

This introduction to symplectic and contact geometry is intended for advanced mathematics undergraduates, graduate students and other interested researchers with some background in differential geometry, manifold theory, and a bit of Lie theory and algebraic topology. Symplectic and contact geometry had their origins in classical mechanics but have developed broadly beyond that. This book stays...

Knots, Links and Their Invariants: An Elementary Course in Contemporary Knot Theory

The textbook Knots, Links and Their Invariants: An Elementary Course in Contemporary Knot Theory by A. B. Sossinsky provides a rigorous, broad, and engaging view of the mathematical landscape of knots and links for a novice student. This textbook highlights many mathematical results that were originally studied using complex tools that are not within reach...

Book cover: "Knots, Links and Their Invariants" by A. B. Sossinsky, featuring a drawing of a snake forming a knot. Student Mathematical Library, Volume 101.

Topics in Cyclic Theory

In various lecture courses given at Oxford University, Quillen introduces and develops cyclic cohomology and its many applications. His presentation emphasizes analysis and differential geometry – a companion volume Topology and K-Theory: Lectures by Daniel Quillen edited by Robert Penner focuses on topology and homological algebra. The editor of this volume, Gordon Blower, has brought together several...

Book cover of Topics in Cyclic Theory by Daniel G. Quillen and Gordon Blower. The cover is a solid blue cover with the title in white.

Advanced Mathematics: An Invitation in Preparation for Graduate School

The intended readers of this book are advanced undergraduates or beginning graduate students. The author’s goal is to present a view of the broad scope of mathematics. In content, it has some similarities to All the Math You Missed, but the latter is aimed somewhat more at preparing future graduate students for what they will encounter in...

Basic Topology 1

Basic Topology 1 by Avishek Adhikari and Mahima Ranjan Adhikari is the first in a series of three books intended as an introduction to various aspects of topology and its applications to other fields of mathematics. The present volume is dedicated to metric spaces and general topology, with Volume 2 covering topological groups, manifolds, and Lie...

Separation in Point-Free Topology

Topology, classically, is commonly considered in flavors, two of which are point-set topology and algebraic topology. These two flavors are so distinct, each with very different toolsets and driving problems, that it would only be a minor exaggeration to say that the only thing they have in common is the underlying notion of what a...

Topology: An Invitation

Topology traces its rich history all the way back to centuries-old ideas of Leibniz and Euler. The precise definition of a topological space is of course of a more recent vintage, and the evolution of the subject across the intervening 300+ years is not only a compelling story, but also a useful source of motivation...

Generalized Ricci Flow

The book Generalized Ricci Flow by Mario Garcia-Fernandez and Jeffrey Streets is an invitation and literature guide to “generalized geometry” and its connections to curvature flow and the existence of metrics with special curvature. The intended reader is a working mathematician or advanced graduate student conversant with smooth real manifolds, and familiar with Kähler metrics, symplectic structures, and parabolic PDEs. “Classical geometry” connotes here the mathematical...

Cover of the book "Generalized Ricci Flow" by Mario Garcia-Fernandez and Jeffrey Streets, part of the University Lecture Series (Volume 76) published by the American Mathematical Society (AMS). The background features a gradient of blue to red with faint mathematical symbols scattered throughout.

Lie Models in Topology

The book under review completely solves an old and monumental problem in topology and was awarded the Ferran Sunyer i Balaguer Prize in 2020. Here’s the backstory. A bit more than half-a-century ago, for various reasons, topologists came to believe that if torsion could be removed from their beloved algebraic invariants (e.g. homotopy and homology...

Cover of the book "Lie Models in Topology" by Urtzi Buijs, Yves Félix, Aniceto Murillo, and Daniel Tanré. The design features a deep green background with white and red text. It is part of the "Progress in Mathematics" series (volume 335) published by Birkhäuser. Logos for the Fundación Ramón Areces and Birkhäuser appear at the bottom.

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