From groups to geometry and back
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 -- Provided by publisher.
Read More ↓Title Statements
- Full title :From groups to geometry and back / Vaughn Climenhaga, Anatole Katok.
Summary
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 -- Provided by publisher.
Read More ↓Edition Statements
- Publication Date:2017
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:United States
- Language:eng
- Publication Date:2017
Notes
"Mathematics Advanced Study Semesters."
The Physical Object
- Description:xix, 420 pages : : illustrations ; : 22 cm.
Edition Identifiers
- ISBN:9781470434793, 1470434792
- oclc:ocn959373143
- LC Classification:QA174.2
- Dewey Decimal:512/.2
Table of Contents
Elements of group theory -- Symmetry in the Euclidean world: Groups of isometries of planar and spatial objects -- Groups of matrices: Linear algebra and symmetry in various geometries -- Fundamental group: A different kind of group associated to geometric objects -- From groups to geometric objects and back -- Groups at large scale -- Hints to selected exercises -- Suggestions for projects and further reading -- Bibliography -- Index.
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