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We study bordism groups and bordism homology theories based on pseudomanifolds and stratified pseudomanifolds. The main seam of the paper demonstrates that when we uses classes of spaces determined by local link properties, the stratified and unstratified bordism theories are identical; this includes the known examples of pseudomanifold bordism theories, such as bordism of Witt spaces and IP spaces. Along the way, we relate the stratified and unstratified points of view for describing various (stratified) pseudomanifold classes.
It is one of the most important facts in 4-dimensional topology that not every spherical homology class of a 4-manifold can be represented by an embedded sphere. In 1978, M. Freedman and R. Kirby showed that in the simply connected case, many of the
We generalize the PL intersection product for chains on PL manifolds and for intersection chains on PL stratified pseudomanifolds to products of locally finite chains on non-compact spaces that are natural with respect to restriction to open sets. Th
This note corrects an error in the char(K)=2 case of the authors computation of the bordism groups of K-Witt spaces for the field K.
Given a monoidal $infty$-category $C$ equipped with a monoidal recollement, we give a simple criterion for an object in $C$ to be dualizable in terms of the dualizability of each of its factors and a projection formula relating them. Predicated on th
We realize Stasheffs multiplihedron geometrically as the moduli space of stable quilted disks. This generalizes the geometric realization of the associahedron as the moduli space of stable disks. We show that this moduli space is the non-negative rea