Ross Geoghegan – författare

Aimed at advanced undergraduates and graduate students, this book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit. The author has included material which isn't covered in other textbooks. Much of the material will be of interest to group theorists who would like to know more about the topological side of their subject, as well as manifold topologists looking for basic material on proper homotopy and finite homology.

Aimed at advanced undergraduates and graduate students, this book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit. The author has included material which isn't covered in other textbooks. Much of the material will be of interest to group theorists who would like to know more about the topological side of their subject, as well as manifold topologists looking for basic material on proper homotopy and finite homology.

Aimed at advanced undergraduates and graduate students, this book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit. The author has included material which isn't covered in other textbooks. Much of the material will be of interest to group theorists who would like to know more about the topological side of their subject, as well as manifold topologists looking for basic material on proper homotopy and finite homology.

The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student's previous intuitive knowledge is placed on solid intellectual ground. The topics covered include: integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets. Methods, such as axiom, theorem and proof, are taught while discussing the mathematics rather than in abstract isolation. Some of the proofs are presented in detail, while others (some with hints) may be assigned to the student or presented by the instructor. The authors recommend that the two parts of the book -- Discrete and Continuous -- be given equal attention.The book ends with short essays on further topics suitable for seminar-style presentation by small teams of students, either in class or in a mathematics club setting. These include: continuity, cryptography, groups, complex numbers, ordinal number, and generating functions.

The Art of Proof is designed for a one-semester or two-quarter course. A typical student will have studied calculus (perhaps also linear algebra) with reasonable success. With an artful mixture of chatty style and interesting examples, the student''s previous intuitive knowledge is placed on solid intellectual ground. The topics covered include: integers, induction, algorithms, real numbers, rational numbers, modular arithmetic, limits, and uncountable sets. Methods, such as axiom, theorem and proof, are taught while discussing the mathematics rather than in abstract isolation. Some of the proofs are presented in detail, while others (some with hints) may be assigned to the student or presented by the instructor. The authors recommend that the two parts of the book -- Discrete and Continuous -- be given equal attention.The book ends with short essays on further topics suitable for seminar-style presentation by small teams of students, either in class or in a mathematics club setting. These include: continuity, cryptography, groups, complex numbers, ordinal number, and generating functions.

This volume contains the proceedings of the AMS Special Session on Ends and Boundaries of Groups, held in honor of Michael Mihalik's 70th birthday, from April 15-16, 2023, at the University of Cincinnati, Cincinnati, Ohio. The papers cover current topics in geometric group theory and related topology. Four survey papers discuss hyperbolic actions, CAT(0) groups, Thompson-type groups and $Z$-set boundaries. Other papers cover new material related to hyperbolic groups, Poincare Duality groups, outer automorphism groups, right angled Artin groups, and mapping class groups. Several papers present new results on ends of spaces and related group theory. A notable addition, intended for readers interested in the interplay of topology and group theory, is a self-contained detailed exposition of $Z$-sets and their role in geometric group theory.