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Volumes of Nullhomotopies in Nilpotent Spaces
Kyle Hansen
https://arxiv.org/abs/2510.00159 https://arxiv.org/pdf/2510.00159

Volumes of Nullhomotopies in Nilpotent Spaces
The Shadowing Principle of Manin has proved a valuable tool for addressing questions of quantitative topology raised by Gromov in the late 1900s. The principle informally provides a way for bounded algebraic maps between differential graded algebras to be translated into nearby genuine maps between their geometric realizations. We extend this principle to finite towers of principal $K(G,n)$ fibrations, and in particular apply this construction to nilpotent spaces. As a specific application of t…