An Invitation to Coarse Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Invitation to Coarse Groups write by Arielle Leitner. This book was released on 2024-01-13. An Invitation to Coarse Groups available in PDF, EPUB and Kindle. 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. The book will primarily be of interest to researchers and graduate students in geometric group theory, topology, category theory and functional analysis, but some parts will also be accessible to advanced undergraduates.
An Invitation to Quantum Cohomology
An Invitation to Quantum Cohomology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Invitation to Quantum Cohomology write by Joachim Kock. This book was released on 2007-12-27. An Invitation to Quantum Cohomology available in PDF, EPUB and Kindle. Elementary introduction to stable maps and quantum cohomology presents the problem of counting rational plane curves Viewpoint is mostly that of enumerative geometry Emphasis is on examples, heuristic discussions, and simple applications to best convey the intuition behind the subject Ideal for self-study, for a mini-course in quantum cohomology, or as a special topics text in a standard course in intersection theory
Progress in Group Field Theory and Related Quantum Gravity Formalisms
Progress in Group Field Theory and Related Quantum Gravity Formalisms - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Progress in Group Field Theory and Related Quantum Gravity Formalisms write by Steffen Gielen. This book was released on 2020-07-01. Progress in Group Field Theory and Related Quantum Gravity Formalisms available in PDF, EPUB and Kindle. Following the fundamental insights from quantum mechanics and general relativity, geometry itself should have a quantum description; the search for a complete understanding of this description is what drives the field of quantum gravity. Group field theory is an ambitious framework in which theories of quantum geometry are formulated, incorporating successful ideas from the fields of matrix models, ten-sor models, spin foam models and loop quantum gravity, as well as from the broader areas of quantum field theory and mathematical physics. This special issue collects recent work in group field theory and these related approaches, as well as other neighbouring fields (e.g., cosmology, quantum information and quantum foundations, statistical physics) to the extent that these are directly relevant to quantum gravity research.
Coarse Geometry of Topological Groups
Coarse Geometry of Topological Groups - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Coarse Geometry of Topological Groups write by Christian Rosendal. This book was released on 2021-12-16. Coarse Geometry of Topological Groups available in PDF, EPUB and Kindle. Provides a general framework for doing geometric group theory for non-locally-compact topological groups arising in mathematical practice.
What's Next?
What's Next? - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook What's Next? write by Dylan Thurston. This book was released on 2020-07-07. What's Next? available in PDF, EPUB and Kindle. William Thurston (1946–2012) was one of the great mathematicians of the twentieth century. He was a visionary whose extraordinary ideas revolutionized a broad range of areas of mathematics, from foliations, contact structures, and Teichmüller theory to automorphisms of surfaces, hyperbolic geometry, geometrization of 3-manifolds, geometric group theory, and rational maps. In addition, he discovered connections between disciplines that led to astonishing breakthroughs in mathematical understanding as well as the creation of entirely new fields. His far-reaching questions and conjectures led to enormous progress by other researchers. In What's Next?, many of today's leading mathematicians describe recent advances and future directions inspired by Thurston's transformative ideas. This book brings together papers delivered by his colleagues and former students at "What's Next? The Mathematical Legacy of Bill Thurston," a conference held in June 2014 at Cornell University. It discusses Thurston's fundamental contributions to topology, geometry, and dynamical systems and includes many deep and original contributions to the field. Incisive and wide-ranging, the book explores how he introduced new ways of thinking about and doing mathematics—innovations that have had a profound and lasting impact on the mathematical community as a whole—and also features two papers based on Thurston's unfinished work in dynamics.
