Quantitative PL bordism
Geometric Topology
2026-02-25 v2 Algebraic Topology
Metric Geometry
Abstract
We study PL bordism theories from a quantitative perspective. Such theories include those of PL manifolds, ordinary homology theory, as well as various more exotic theories such as bordism of Witt spaces. In all these cases we show that a null-bordant cycle of bounded geometry and simplices has a filling of bounded geometry whose number of simplices is slightly superlinear in . This bound is similar to that found in our previous work on smooth cobordism.
Cite
@article{arxiv.2311.16389,
title = {Quantitative PL bordism},
author = {Fedor Manin and Bena Tshishiku and Shmuel Weinberger},
journal= {arXiv preprint arXiv:2311.16389},
year = {2026}
}
Comments
47 pages, 1 figure, 2 tables. Major changes in v2: Theorem 2.2 is new. Many corrections in Section 4. Appendix B is vastly expanded and is now joint with Bena Tshishiku; ultimately this may become a separate paper