scholarly journals Ribbon cobordisms between lens spaces

2021 ◽  
Vol 315 (1) ◽  
pp. 111-128
Author(s):  
Marius Huber
Keyword(s):  
Lens Spaces

Isometry classes of 3 dimensional lens spaces

2002 ◽  
Vol 13 (7) ◽  
pp. 295-299
Author(s):  
Michel Cahen ◽  
Mohamed Chaibi
Keyword(s):  
Lens Spaces ◽  
3 Dimensional

On the cohomology of orbit space of free ℤ p -actions on lens spaces

2007 ◽  
Vol 117 (3) ◽  
pp. 287-292 ◽  
Author(s):  
Hemant Kumar Singh ◽  
Tej Bahadur Singh
Keyword(s):  
Orbit Space ◽  
Lens Spaces

Topology of ambient manifolds of non-singular Morse – Smale flows with three periodic orbits

2021 ◽  
Vol 29 (6) ◽  
pp. 863-868
Author(s):  
Danila Shubin ◽  
◽  
Keyword(s):  
Periodic Orbits ◽  
Three Dimensional ◽  
Solid Torus ◽  
Lens Space ◽  
Tubular Neighborhood ◽  
Lens Spaces ◽  
Ambient Manifold ◽  
Orientable Manifold ◽  
Smale Flows ◽  
Published Result

The purpose of this study is to establish the topological properties of three-dimensional manifolds which admit Morse – Smale flows without fixed points (non-singular or NMS-flows) and give examples of such manifolds that are not lens spaces. Despite the fact that it is known that any such manifold is a union of circular handles, their topology can be investigated additionally and refined in the case of a small number of orbits. For example, in the case of a flow with two non-twisted (having a tubular neighborhood homeomorphic to a solid torus) orbits, the topology of such manifolds is established exactly: any ambient manifold of an NMS-flow with two orbits is a lens space. Previously, it was believed that all prime manifolds admitting NMS-flows with at most three non-twisted orbits have the same topology. Methods. In this paper, we consider suspensions over Morse – Smale diffeomorphisms with three periodic orbits. These suspensions, in turn, are NMS-flows with three periodic trajectories. Universal coverings of the ambient manifolds of these flows and lens spaces are considered. Results. In this paper, we present a countable set of pairwise distinct simple 3-manifolds admitting NMS-flows with exactly three non-twisted orbits. Conclusion. From the results of this paper it follows that there is a countable set of pairwise distinct three-dimensional manifolds other than lens spaces, which refutes the previously published result that any simple orientable manifold admitting an NMS-flow with at most three orbits is lens space.

Lens Spaces

1973 ◽  
pp. 85-101
Author(s):  
Marshall M. Cohen
Keyword(s):  
Lens Spaces

scholarly journals Symplectic fillings of lens spaces as Lefschetz fibrations

2016 ◽  
Vol 18 (7) ◽  
pp. 1515-1535 ◽  
Author(s):  
Mohan Bhupal ◽  
Burak Ozbagci
Keyword(s):  
Lens Spaces ◽  
Lefschetz Fibrations

The Milnor–Stasheff Filtration on Spaces and Generalized Cyclic Maps

2012 ◽  
Vol 55 (3) ◽  
pp. 523-536 ◽  
Author(s):  
Norio Iwase ◽  
Mamoru Mimura ◽  
Nobuyuki Oda ◽  
Yeon Soo Yoon
Keyword(s):  
Projective Spaces ◽  
Intermediate Stage ◽  
Lens Spaces ◽  
Cyclic Maps

AbstractThe concept of Ck-spaces is introduced, situated at an intermediate stage between H-spaces and T-spaces. The Ck-space corresponds to the k-th Milnor–Stasheff filtration on spaces. It is proved that a space X is a Ck-space if and only if the Gottlieb set G(Z, X) = [Z, X] for any space Z with cat Z ≤ k, which generalizes the fact that X is a T-space if and only if G(ΣB, X) = [ΣB, X] for any space B. Some results on the Ck-space are generalized to the -space for a map ƒ : A → X. Projective spaces, lens spaces and spaces with a few cells are studied as examples of Ck-spaces, and non-Ck-spaces.

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