Topology – Page 2 – Mathematical Association of America

Featured Resources

Low Stakes, High Rewards: How a Corequisite Course Improved Student Performance in Intro to Proofs

By Ekaterina Yurasovskaya With its highly abstract material and proof-writing that students encounter for the first time, Introduction to Proofs often turns into a gatekeeper to a mathematics major. At the Mathematics Department at Seattle University, we achieved significant results by creating a lecture-free, problem-solving ungraded co-requisite course called Mathematical Communication and Reasoning (MCR). The new...

When Water Isn’t Really Water

By Lew Ludwig The hamburger graph has become my unexpected companion this summer. It first appeared in a workshop I was co-facilitating, comparing the water usage of AI prompts to beef production. Then it surfaced again a few weeks later - and that's when I realized we weren't really arguing about water at all. The first...

An Elementary Overview of Mathematical Structures

There is much that is appealing about making explicit the categorical connections between different mathematical subjects. To connect what we know about functions of sets to what we know about homomorphisms of groups to what we know about continuous functions of topological spaces and so forth is the epitome of pattern recognition. And that is...

Cover of the book "An Elementary Overview of Mathematical Structures: Algebra, Topology and Categories" by Marco Grandis. The design features clean, modern typography with blue and orange text on a white background. Flowing blue wave graphics decorate the bottom portion, symbolizing abstract structure and continuity. Published by World Scientific.

The Shape of Space

First published in 1985, The Shape of Space is an introduction to the low-dimensional geometry and topology necessary to discuss what is currently known about the topological shape of the universe. What makes this book so remarkable is that it is able to do all of this while remaining accesible to an extremely broad audience: the book...

Topology: A Categorical Approach

Instructors of advanced undergraduate and beginning graduate topology courses find themselves with a happy dilemma of having several well-written texts to choose from to accompany their lectures. Topology by Munkres, Introduction to Topological Manifolds by Lee, and Elementary Topology Problem Textbook by Viro et al., are just a few notable options. Topology: A Categorical Approach aims to extend this selection even further. The topological material it presents is fairly standard,...

Cover of the book "Topology: A Categorical Approach" by Tai-Danae Bradley, Tyler Bryson, and John Terilla. The design features an abstract, dynamic pattern of light trails in red, white, and blue tones against a dark background, conveying a modern and conceptual feel. The title is in red and white text at the top left, with author names in white at the bottom left.

Lectures on Contact 3-Manifolds, Holomorphic Curves and Intersection Theory

This book is an introduction to the intersection theory of punctured J-holomorphic curves in symplectic 4-manifolds with boundary and applications to symplectic cobordisms and fillings of contact 3-manifolds. The main theme of the text is the use of the moduli space and intersection theory of punctured J-holomorphic curves to understand the structure of a symplectic 4-manifold, locally as a foliation and globally as a...

Lectures on Factorization Homology, ∞-Categories, and Topological Field Theories

Each of the three subjects in the title can serve as the title for a rather thick book. In fact, the latter two already do. Factorization homology, a homology theory for manifolds, is a relatively new and hot topic of research. While a single book devoted to it is not (yet) in existence, there is certainly a growing...

Lectures on Field Theory and Topology

Mathematics and physics have always had a close connection, the needs of one sometimes dictating the direction of the other. Witten’s introduction of topological quantum field theories (TQFTs) in the 1980s led to Atiyah’s axiomatization of TQFTs and from there to a renaissance of physical thinking in geometry and topology. An apotheosis of this particular area...

Topology of Polymers

Every generation since the Victorian era must have seemed like the Age of Materials. From Stanislas Sorel's artificial ivory through artificial dyes, artificial fibres, the plastic revolution, to ceramic superconductors, it's been one age of materials after another. And that is unlikely to change, for many of our major technological challenges - from containing fusion to manipulating nanostructures - are problems...

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