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math.DG2025
Stratified manifolds with corners
Dominic Joyce
We define categories of stratified manifolds (s-manifolds) and stratified manifolds with corners (s-manifolds with corners). An s-manifold of dimension is a Hausdorff,…
math.AT2025
Bordism categories and orientations of moduli spaces
Dominic Joyce, Markus Upmeier
To define enumerative invariants in geometry, one often needs orientations on moduli spaces of geometric objects. This monograph develops a new bordism-theoretic point of view on o…