Algebra/Topology Seminar

Speaker: Anssi Lahtinen

Title: A theory of twisted umkehr maps

Abstract: Informally, umkehr maps — also variously called Gysin maps, wrong-way maps, shriek maps, integration along fibre maps, pushforward maps and dimension-shifting transfer maps — are induced maps pointing in the opposite direction from the usual induced maps in the context. In this talk, I will discuss my recent work on a theory of umkehr maps. In this theory, suited for twisted generalized homology theories but also of interest in the untwisted context, interesting umkehr maps, including important classical ones, arise from maps defined in terms of category-theoretical universal properties. This makes it possible to access these maps in terms of such universal properties, facilitating formal arguments divorced from the often messy details of particular constructions of umkehr maps.