Workshop on the h-principle and beyond
A Controlled Mather Thurston Theorem
Abstract: The "c-principle" is a cousin of Gromov's h-principle in which cobordism rather than homotopy is required to (canonically) solve a problem. We show that for the MT-theorem, when the base dimensions is not equal four, only the mildest cobordisms, semi-s-cobordisms, are required. In a physical context, the extra topology (a perfect fundamental group) these cobordisms introduce could be hidden in the UV, suggesting that the action for gauge theories might be formulated in terms of group extensions and flat connections, rather than curvature. See arXiv:2006.00374 for some preliminary results.