Best Reference Books – Algebraic Topology

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We have compiled the list of Top 10 Best Reference Books on Algebraic Topology subject. These books are used by students of top universities, institutes and colleges. Here is the full list of top 10 best books on Algebraic Topology along with reviews.

Kindly note that we have put a lot of effort into researching the best books on Algebraic Topology subject and came out with a recommended list of top 10 best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on "Algebraic Topology" as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.

1. “Introduction to Functional Analysis” by A Taylor and D Lay

“Introduction to Functional Analysis” Book Review: The book is a well-structured and self-contained piece of writing featuring the theory of normed linear spaces and of linear mappings. It aims in providing the essential base for further study in many areas of analysis. The chapters based on Banach algebras, material on weak topologies and duality, equicontinuity, Krein-Milman theorem, and theory of Fredholm operators are included in this book. The book also highlights the problems faced in linear algebra, classical analysis, and differential and integral equations.

2. “Collectively Compact Operator Approximation Theory” by P M Anselone
3. “Introduction to Functional Analysis” by A H Siddiqi

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“Introduction to Functional Analysis” Book Review: The book aims at presenting the major aspects and important topics of functional analysis. The chapters of this book reflect basic theorems dealing with properties of functional and operators namely, Hahn-Banach theorem, Banach-Steinhaus theorem, Open mapping theorem and Closed graph theorem. The book also highlights the applications of functional analysis in operator equations, boundary value problems, optimization, variational inequalities, finite element methods, optimal control, and wavelets. The students and professionals seeking deep information in functional analysis will find this text helpful.

4. “Algebraic Topology” by Allen Hatcher

“Algebraic Topology” Book Review: The book delicately focuses students, researchers, professionals, engineers in the development of algebraic topology. All the basic concepts of algebraic topology are covered in this text, hence making it an ideal choice for self-study. The chapters of this book cover all the major topics of fundamental group and covering spaces, homology and cohomology, higher homotopy groups, and homotopy theory. The content of this book is supported with many examples and exercises. This book will be useful for students and teachers.

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5. “Algebraic Topology: A First Course” by William Fulton

“Algebraic Topology: A First Course” Book Review: The book presents important concepts and topics of algebraic topology along with their applications in various areas of mathematics. The chapters of this book describe topics like relation between homology and integration, plane domains, Riemann surfaces, winding numbers, degrees of mappings, and fixed-point theorems. Various applications of algebraic topology namely, Jordan curve theorem and invariance of domain are included in this text. The book will be beneficial for the students of mathematics and science.

6. “Algebraic Topology” by C R F Maunder

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“Algebraic Topology” Book Review: The book aims at presenting basic algebraic topology from a homotopy theoretical point-of-view. The chapters of this book feature construction homology or homotopy groups of a topological space, homotopy theory, CW-complexes, and co-homology groups associated with a general Ω-spectrum. The applications of algebraic topology to various topological problems such as classification of surfaces and duality theorems for manifolds are highlighted in this book. For better understanding of the readers many examples and exercises are included in this text. The book will be valuable for the undergraduate and first-year graduate students of related to homotopy or homology theory.

7. “Algebraic Topology” by Robert M Switzer

“Algebraic Topology” Book Review: The book is a contemporary piece of writing presenting the latest topics and untouched aspects of homotopy and homology. The chapters of this book are comprehensive, precise, and revolve around homotopy groups of sphere and computation of various cobordism groups. The stable homotopy theory is featured in this book along with its basic concepts, principle methods, and applications in different fields. The book will be a good resource for the professionals and experts in the field of algebraic topology.

8. “A Concise Course in Algebraic Topology” by J P May

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“A Concise Course in Algebraic Topology” Book Review: The book will be suitable for the teachers and advanced graduate students of mathematics. The chapters of this book are well-structured, self-contained, and deliver deep information on various topics of algebraic topology. The later section of the book portrays the sketches of substantial areas of algebraic topology. The applications of algebraic topology in various advanced fields namely geometry, topology, differential geometry, algebraic geometry and lie groups are highlighted in this piece of writing. The book consists of numerous problems for self-study and self-assessment of the readers.

9. “Basic Algebraic Topology” by Anant R Shastri

“Basic Algebraic Topology” Book Review: The book reflects deep information on real analysis, point-set topology, and basic algebra. It is broadly classified into three sections featuring introduction of algebraic topology, cell complexes and simplicial complexes, and covering spaces and fundamental groups, respectively. The Poincaré duality, De Rham theorem, cohomology of sheaves, Čech cohomology is discussed in detail. The topics like higher homotopy groups, Hurewicz’s isomorphism theorem, obstruction theory, Eilenberg-MacLane spaces, and Moore-Postnikov decomposition are thoroughly explained. The content of this book is enriched with several exercises and applications of algebraic topology. The book will be appropriate for the graduate students, researchers, and working mathematicians related to the field of algebraic topology.

10. “Elements of Algebraic Topology” by James R Munkres

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“Elements of Algebraic Topology” Book Review: The book aims in providing readers a strong foundation in the field of algebraic topology. The chapters of this book are reader-friendly, self-contained, and contain a detailed description of homology and cohomology theory, universal coefficient theorems, Kunneth theorem, and duality in manifolds. The applications of algebraic topology in the classical theorems of point-set topology are clearly mentioned in this book. The book will be a great source of information for the beginners in algebraic topology, as it explains the complex and advanced topics, quite efficiently.

People who are searching for Free downloads of books and free pdf copies of these top 10 books on Algebraic Topology – we would like to mention that we don’t have free downloadable pdf copies of these good books and one should look for free pdf copies from these Authors only if they have explicitly made it free to download and read them.

We have created a collection of best reference books on "Algebraic Topology" so that one can readily see the list of top books on "Algebraic Topology" and buy the books either online or offline.

If any more book needs to be added to the list of best books on Algebraic Topology subject, please let us know.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter