Generalized plumbings and Murasugi sums
Geometric Topology
2016-03-22 v2 Symplectic Geometry
Abstract
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 or contact topology.
Cite
@article{arxiv.1412.2229,
title = {Generalized plumbings and Murasugi sums},
author = {Burak Ozbagci and Patrick Popescu-Pampu},
journal= {arXiv preprint arXiv:1412.2229},
year = {2016}
}
Comments
54 pages, 31 figures. We revised the first version according to the referee's comments