Simon Scott - Microlocal and Global Analysis, I...
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Simon Scott - Microlocal and Global Analysis, Interactions with Geometry
Fibre-oriented bordism homology and genera.
The set of fibrations over manifold X which are fibrewise bordant has a canonical ring structure with
respect to which a vertical genus is determined by certain combinations of `vertical characteristic classes' taking values
in the singular cohomology of X. Family index densities provide natural examples. It turns out that the structures
involved are governed by a vertical Pontryagin-Thom spectrum and its associated generalised (co)homology. These
themes and, in particular, how the orientation along the fibres is a crucial ingredient, will be the focus of this talk.