Quantitative PL bordism

2023/11/28 by Fedor Manin, Shmuel Weinberger, Manin, Fedor +1 · 1 citation
#math.GT #math.AT #math.MG

paper · pdf · doi:10.48550/arxiv.2311.16389

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 V simplices has a filling of bounded geometry whose number of simplices is slightly superlinear in V. This bound is similar to that found in our previous work on smooth cobordism.

Cited by

• Morse complexity of homology classes

Related

• PL cobordism and classification of PL manifolds
• The geometric cobordism hypothesis
• The homotopy type of the PL cobordism category. I
• Morse-Bott inequalities, Topology Change and Cobordisms to Nothing
• Quantitative bordism over acyclic groups and Cheeger-Gromov ρ-invariants