Abstract
The classifying space of the embedded cobordism category has been identified by Galatius, Tillmann, Madsen and Weiss [Acta. Math. 202 (2009) 195–239] as the infinite loop space of a certain Thom spectrum. This identifies the set of path components with the classical cobordism group. In this paper, we give a geometric interpretation of the higher homotopy groups as certain cobordism groups where all manifolds are now equipped with a set of orthonormal sections in the tangent bundle. We also give a description of the fundamental group as a free group with a set of geometrically intuitive relations.
Citation
Marcel Bökstedt. Anne Marie Svane. "A geometric interpretation of the homotopy groups of the cobordism category." Algebr. Geom. Topol. 14 (3) 1649 - 1676, 2014. https://doi.org/10.2140/agt.2014.14.1649
Information