Generalized Plumbings and Murasugi Sums

Arnold Mathematical Journal - Tập 2 - Trang 69-119 - 2015
Burak Ozbagci1, Patrick Popescu-Pampu2
1Department of Mathematics, Koç University, Sarıyer, Turkey
2Université Lille 1, UFR de Maths., Villeneuve d’Ascq Cedex, France

Tóm tắt

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. We conclude with several open questions relating this work with singularity theory and contact topology.

Tài liệu tham khảo

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