Generalized Plumbings and Murasugi Sums

Ozbagci, Burak; Popescu-Pampu, Patrick

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1007/s40598-015-0033-3

Title :

Generalized Plumbings and Murasugi Sums

Author(s) :

Ozbagci, Burak [Auteur]
Koç University
Popescu-Pampu, Patrick [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Arnold Mathematical Journal

Pages :

69-119

Publisher :

Springer

Publication date :

2016-03

ISSN :

2199-6792

English keyword(s) :

Cobordisms
Morse functions
Murasugi sums
Open books
Plumbing
Seifert surfaces

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

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