seminar: YOUNG SEMINAR: Arrangement of Submanifolds and the Tangent-Bundle Complement
speaker: Priyavrat Deshpande (The University of Western Ontario, London, Canada)abstract: A real arrangement of hyperplanes is a collection of finitely many hyperplanes in a real vector space. It is known that the combinatorics of the intersections of these hyperplanes contains substantial information about the topology of the complement of the hyperplanes in the real as well as complexified space. For example, the cohomology of the complexified complement can be expressed in terms of the intersection lattice associated with the arrangement. The face poset of an arrangement defines a cell complex (the Salvetti complex) which has the homotopy type of this complement. In the same spirit, I will define the notion of an arrangement of submanifolds and its complexification. The goal is to investigate whether the combinatorics of the intersections of these submanifolds offer insight about the topology of the 'real' complementand the tangent bundle complement, an analogue of the complexified complement. The aim of this talk is to introduce these notions and report recent developments that generalize the theory of (real) hyperplane arrangements.
timetable:
Thu 10 Jun, 17:00 - 18:00, Sala Conferenze Centro De Giorgi
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