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Homogeneous length
functions on groups
Tobias Fritz, Siddhartha Gadgil, Apoorva Khare, Pace P. Nielsen, Lior Silberman and Terence Tao |
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Vol. 12 (2018), No. 7, 1773–1786
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Abstract |
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A pseudolength function defined on an arbitrary group is a map obeying , the symmetry property , and the triangle inequality for all . We consider pseudolength functions which saturate the triangle inequality whenever , or equivalently those that are homogeneous in the sense that for all . We show that this implies that for all . 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. |
Keywords
homogeneous length function, pseudolength function,
quasimorphism, Banach space embedding
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Mathematical Subject Classification 2010
Primary: 20F12
Secondary: 20F65
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Milestones
Received: 11 January 2018
Revised: 20 April 2018
Accepted: 12 June 2018
Published: 27 October 2018
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Authors |
| Tobias Fritz | |
| Max Planck Institute for Mathematics
in the Sciences Leipzig Germany |
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| Siddhartha Gadgil | |
| Department of Mathematics Indian Institute of Science Bangalore India |
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| Apoorva Khare | |
| Department of Mathematics Indian Institute of Science Bangalore India |
Analysis and Probability Research
Group Indian Institute of Science Bangalore India |
| Pace P. Nielsen | |
| Department of Mathematics Brigham Young University Provo, UT United States |
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| Lior Silberman | |
| University of British Columbia Vancouver BC Canada |
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| Terence Tao | |
| Department of Mathematics University of California Los Angeles Los Angeles, CA United States |
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