Coxeter Groups

Adam Piggott

doi:10.2307/j.ctt1vwmg8g.17

Coxeter Groups

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

As this book has shown so far, in geometric group theory we study groups and geometric spaces simultaneously, linking them via group actions. Sometimes we start with a family of spaces, and we try to find groups that act on the spaces in a prescribed way. Other times we start with a family of groups, and we try to find spaces on which they act in a prescribed way. Here, I tell a story that follows first one of these approaches, and then the other. We shall see that one way to find a space on which a group acts is to build a space, readymade for the purpose, using combinatorics from the group.

Original language	English
Title of host publication	Office Hours with a Geometric Group Theorist
Editors	Matt Clay, Dan Margalit
Place of Publication	US
Publisher	Princeton University Press
Pages	269-290
Volume	1
Edition	1
ISBN (Print)	978-0691158662
DOIs	https://doi.org/10.2307/j.ctt1vwmg8g.17
Publication status	Published - 2017

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10.2307/j.ctt1vwmg8g.17

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title = "Coxeter Groups",

abstract = "As this book has shown so far, in geometric group theory we study groups and geometric spaces simultaneously, linking them via group actions. Sometimes we start with a family of spaces, and we try to find groups that act on the spaces in a prescribed way. Other times we start with a family of groups, and we try to find spaces on which they act in a prescribed way. Here, I tell a story that follows first one of these approaches, and then the other. We shall see that one way to find a space on which a group acts is to build a space, readymade for the purpose, using combinatorics from the group.",

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AB - As this book has shown so far, in geometric group theory we study groups and geometric spaces simultaneously, linking them via group actions. Sometimes we start with a family of spaces, and we try to find groups that act on the spaces in a prescribed way. Other times we start with a family of groups, and we try to find spaces on which they act in a prescribed way. Here, I tell a story that follows first one of these approaches, and then the other. We shall see that one way to find a space on which a group acts is to build a space, readymade for the purpose, using combinatorics from the group.

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Coxeter Groups

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