Interlevel persistence and Floer theory

Date: 2022-06-30

Time: 16:15 - 17:15

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Michael Usher


Various versions of filtered Floer theory give rise to persistence modules whose structure maps mimic the relationship between the homologies of the sublevel sets of a Morse function on a finite-dimensional manifold.  In the finite-dimensional case, it can be useful to consider not just sublevel sets but interlevel sets (preimages of general intervals, including singletons); these fit into a different type of persistence module structure which is classified by a barcode that carries strictly more information than the sublevel persistence barcode.  I will explain a way of obtaining such interlevel barcodes from a general algebraic setup which applies to situations such as Hamiltonian Floer theory in which there is an appropriate version of Poincaré duality, even if an obvious analogue of the interlevel sets is missing.