Urysohn Width and Surgeries

TL;DR

This paper investigates how Urysohn width behaves under surgeries and connected sums of manifolds, providing bounds, extending to universal covers, and demonstrating the optimality of constants with examples.

Contribution

It introduces bounds on Urysohn width under surgeries, extends analysis to universal covers, and establishes the optimality of constants with concrete examples.

Findings

Bounds on Urysohn width for connected sums

Extension of results to universal covers

Examples demonstrating optimality of constants

Abstract

We analyze the behavior of Urysohn width of manifolds under a connected sum operation, specifically, bounding widths of summands in terms of widths of the sum and vice versa. Our methods also apply to the universal covers of these spaces, and to more general type of surgeries. Lastly, we provide examples that show the optimality of constants in our estimates.