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2018-02-19  02:03 hrs.

Generalized plumbings and Murasugi sums

Patrick Popescu-Pampu
Universite de Lille 1


I will present joint work with Burak Ozbagci. We propose a generalization of the classical notions of plumbing and Murasugi summing operations to smooth manifolds of arbitrary dimensions, so that in this general context Gabai's credo "the Murasugi sum is a natural geometric operation" holds. In particular, we prove that the sum of the pages of two open books is again a page of an open book and that there is an associated summing operation of Morse maps. I will conclude with several open questions relating our work with singularity theory or contact topology.




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