Fritz, Tobias and Gadgil, Siddhartha and Khare, Apoorva and Nielsen, Pace P and Silberman, Lion and Tao, Terence
(2018)
*Homogeneous length functions on groups.*
In: ALGEBRA & NUMBER THEORY, 12
(7).
pp. 1773-1786.

## Abstract

A pseudolength function defined on an arbitrary group G = (G, . , e, ()(-1)) is a map l : G -> 0, +infinity) obeying l(e) = 0, the symmetry property l (x(-1)) = l(x), and the triangle inequality l(xy) <= l(x) + l(y) for all x, y is an element of G. We consider pseudolength functions which saturate the triangle inequality whenever x = y, or equivalently those that are homogeneous in the sense that l(x(n)) = nl(x) for all n is an element of N. We show that this implies that l(x, y]) = 0 for all x, y is an element of G. This leads to a classification of such pseudolength functions as pullbacks from embeddings into a Banach space. We also obtain a quantitative version of our main result which allows for defects in the triangle inequality or the homogeneity property.

Item Type: | Journal Article |
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Additional Information: | Copy right for this article belong to MATHEMATICAL SCIENCE PUBL |

Keywords: | homogeneous length function; pseudolength function; quasimorphism; Banach space embedding |

Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |

Depositing User: | Id for Latest eprints |

Date Deposited: | 30 Nov 2018 14:49 |

Last Modified: | 30 Nov 2018 14:49 |

URI: | http://eprints.iisc.ac.in/id/eprint/61200 |

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