%0 Generic
%A Rabel, Martin
%C Heidelberg
%D 2022
%F heidok:31297
%R 10.11588/heidok.00031297
%T Homotopically Stratified Cobordism Theories
%U https://archiv.ub.uni-heidelberg.de/volltextserver/31297/
%X This thesis studies the geometric properties related to certain transversality statements on singular spaces, in a purely topological setting. These enter in the main part -- the construction of a generalized homology theory realized via bordism of such singular spaces -- through the inverse of the excision-isomorphism, the most difficult aspect of that problem. The relevancy of this homology theory is due to the unification of both, possessing a geometric description, establishing geometric fundamental-classes, and at the same time being well-suited to study inherently topological phenomena, like homeomorphism-invariance of said fundamental-classes, even in the absence of pl-structures. As an application, the invariance of Goresky--MacPherson L-classes under certain homeomorphisms is demonstrated.