Articles liés à From Groups to Geometry and Back
Synopsis
Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory.
The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras.
The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering spaces and deck transformations. In the other direction, Cayley graphs, planar models, and fundamental domains appear as geometric objects associated to groups. The final chapter discusses groups themselves as geometric objects, including a gentle introduction to Gromov's theorem on polynomial growth and Grigorchuk's example of intermediate growth.
The book is accessible to undergraduate students (and anyone else) with a background in calculus, linear algebra, and basic real analysis, including topological notions of convergence and connectedness.
This book is a result of the MASS course in algebra at Penn State University in the fall semester of 2009.
Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.
À propos de l?auteur
Vaughn Climenhaga, University of Houston, TX.
Anatole Katok, Pennsylvania State University, University Park, PA.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
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From Groups to Geometry and Back
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American Mathematical Society, 2017
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ISBN 13 : 9781470434793
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From Groups to Geometry and Back
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ISBN 13 : 9781470434793
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Paperback. Etat : New. Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory.The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras.The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering spaces and deck transformations. In the other direction, Cayley graphs, planar models, and fundamental domains appear as geometric objects associated to groups. The final chapter discusses groups themselves as geometric objects, including a gentle introduction to Gromov's theorem on polynomial growth and Grigorchuk's example of intermediate growth.The book is accessible to undergraduate students (and anyone else) with a background in calculus, linear algebra, and basic real analysis, including topological notions of convergence and connectedness.This book is a result of the MASS course in algebra at Penn State University in the fall semester of 2009. N° de réf. du vendeur LU-9781470434793
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Climenhaga, V: From Groups to Geometry and Back
Edité par
American Mathematical Society, 2017
ISBN 10 : 1470434792
ISBN 13 : 9781470434793
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Vendeur : moluna, Greven, Allemagne
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Etat : New. Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objec. N° de réf. du vendeur 595975119
Quantité disponible : 1 disponible(s)
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From Groups to Geometry and Back
Edité par
American Mathematical Society, 2017
ISBN 10 : 1470434792
ISBN 13 : 9781470434793
Neuf
Couverture souple
Vendeur : Kennys Bookstore, Olney, MD, Etats-Unis
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From Groups to Geometry and Back
Edité par
American Mathematical Society, US, 2017
ISBN 10 : 1470434792
ISBN 13 : 9781470434793
Neuf
Paperback
Vendeur : Rarewaves.com USA, London, LONDO, Royaume-Uni
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Paperback. Etat : New. Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory.The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras.The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering spaces and deck transformations. In the other direction, Cayley graphs, planar models, and fundamental domains appear as geometric objects associated to groups. The final chapter discusses groups themselves as geometric objects, including a gentle introduction to Gromov's theorem on polynomial growth and Grigorchuk's example of intermediate growth.The book is accessible to undergraduate students (and anyone else) with a background in calculus, linear algebra, and basic real analysis, including topological notions of convergence and connectedness.This book is a result of the MASS course in algebra at Penn State University in the fall semester of 2009. N° de réf. du vendeur LU-9781470434793
Quantité disponible : 1 disponible(s)
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From Groups to Geometry and Back
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ISBN 10 : 1470434792
ISBN 13 : 9781470434793
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From Groups to Geometry and Back
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From Groups to Geometry and Back
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From Groups to Geometry and Back
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From Groups to Geometry and Back
Edité par
American Mathematical Society, 2017
ISBN 10 : 1470434792
ISBN 13 : 9781470434793
Neuf
Couverture souple
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