Round-handle decomposition ofS2×S1

Cordero, Alicia; Alfaro, J. Martínez; Vindel, P.

doi:10.1080/14689360600893793

Cited by 2 publications

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“…In dimension three, only the set of periodic orbits of non singular Morse-Smale systems (NMS) on S 3 (M. Wada [8], K. Yano [9]) and S 2 × S 1 (A. Cordero, J. Martínez Alfaro and P. Vindel [5]) have been characterized in terms of links. These characterizations are based on the round handle decomposition (RHD) introduced by Asimov [1] and Morgan [6].…”

Section: Introductionmentioning

confidence: 99%

NMS Flows on S 3 with no Heteroclinic Trajectories Connecting Saddle Orbits

Campos

Vindel

2012

J Dyn Diff Equat

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Abstract.In this paper we find topological conditions for the non existence of heteroclinic trajectories connecting saddle orbits in non singular Morse-Smale flows on S 3 .We obtain the non singular Morse-Smale flows that can be decomposed as connected sum of flows and we show that these flows are those who have no heteroclinic trajectories connecting saddle orbits. Moreover, we characterize these flows in terms of links of periodic orbits.MSC: 37D15 Keywords: NMS systems, links of periodic orbits, round handle decomposition, connected sum. M. Wada [8, Theorem 1] characterizes the links of periodic orbits of NMS flows on S 3 in terms of six operations and a generator, the hopf link. He states that every link obtained by applying these operations corresponds to the set of periodic orbits of a NMS flow on S 3 . The link of periodic orbits of a NMS flow on S 3 is defined by the cores of the round-handles in the round handle decomposition of the manifold. Although there is a 1-1 correspondence between the flow and the round handle decomposition, this is not the case for the link of periodic orbits. Different round handle decompositions can yield the same link (B. Campos, J. Martínez Alfaro and P. Vindel [2]), but the corresponding flows are not topologically equivalent (B. Campos and P. Vindel [3]). So, the link of periodic orbits does not describe completely the flow. Nevertheless,

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