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An Invitation to Coarse Groups (Lecture Notes in Mathematics, 2339) free ebook download

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Author(s):	Arielle Leitner

Date:	2024	Format:	pdf	Language:	English	ISBN/ASIN:	3031427599
Pages:	263	OCR:		Quality:		ISBN13:
Uploader:	alex21s	Upload Date:	1/19/2024 4:10:21 PM

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3031427599 pdf
This book lays the foundation for a theory of coarse groups: namely, sets with operations that satisfy the group axioms up to uniformly bounded error. These structures are the group objects in the category of coarse spaces, and arise naturally as approximate subgroups, or as coarse kernels.
The first aim is to provide a standard entry-level introduction to coarse groups. Extra care has been taken to give a detailed, self-contained and accessible account of the theory. The second aim is to quickly bring the reader to the forefront of research. This is easily accomplished, as the subject is still young, and even basic questions remain unanswered.
Reflecting its dual purpose, the book is divided into two parts. The first part covers the fundamentals of coarse groups and their actions. Here the theory of coarse homomorphisms, quotients and subgroups is developed, with proofs of coarse versions of the isomorphism theorems, and it is shown how coarse actions are related to fundamental aspects of geometric group theory. The second part, which is less self-contained, is an invitation to further research, where each thread leads to open questions of varying depth and difficulty. Among other topics, it explores coarse group structures on set-groups, groups of coarse automorphisms and spaces of controlled maps. The main focus is on connections between the theory of coarse groups and classical subjects, including: number theory  the study of bi-invariant metrics on groups  quasimorphisms and stable commutator length  groups of outer automorphisms  and topological groups and their actions.
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An Invitation to Coarse Groups (Lecture Notes in Mathematics, 2339) free ebook download

Category: Mathematics

Description: Click to see full description

Category:
Mathematics