# Quantitative nullhomotopy and rational homotopy type

@article{Chambers2016QuantitativeNA,
title={Quantitative nullhomotopy and rational homotopy type},
author={Gregory R. Chambers and F. Manin and S. Weinberger},
journal={Geometric and Functional Analysis},
year={2016},
volume={28},
pages={563-588}
}
• Published 2016
• Mathematics
• Geometric and Functional Analysis
In a 2014 survey, Gromov asks the following question: given a nullhomotopic map $${f:S^{m} \to S^{n}}$$f:Sm→Sn of Lipschitz constant L, how does the Lipschitz constant of an optimal nullhomotopy of f depend on L, m, and n? We establish that for fixed m and n, the answer is at worst quadratic in L. More precisely, we construct a nullhomotopy whose thickness (Lipschitz constant in the space variable) is C(m,n)(L + 1) and whose width (Lipschitz constant in the time variable) is C(m,n)(L + 1)2… Expand
9 Citations

#### References

SHOWING 1-10 OF 22 REFERENCES
Quantitative algebraic topology and Lipschitz homotopy
• Mathematics
• Proceedings of the National Academy of Sciences
• 2013
Edgewise Subdivision of a Simplex
• Computer Science
• Discret. Comput. Geom.
• 2000