scholarly journals Ear Decomposition and Balanced Neighborly Simplicial Manifolds

10.37236/8341 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Hailun Zheng
Keyword(s):  
Lens Space ◽  
Ear Decomposition ◽  
Simplicial Sphere ◽  
Simplicial Manifolds

 We find the first non-octahedral balanced 2-neighborly 3-sphere and the balanced 2-neighborly triangulation of the lens space $L(3,1)$. Each construction has 16 vertices. We show that there exists a balanced 3-neighborly non-spherical 5-manifold with 18 vertices. We also show that the rank-selected subcomplexes of a balanced simplicial sphere do not necessarily have an ear decomposition.

Knots with the Lens Space Surgery

2011 ◽  
Vol 10 (1) ◽  
pp. 561-570
Author(s):  
Alberto Cavicchioli ◽  
Ilaria Telloni
Keyword(s):  
Lens Space

Ear decomposition of 3-regular polyhedral links with applications

2014 ◽  
Vol 359 ◽  
pp. 146-154 ◽  
Author(s):  
Xiao-Sheng Cheng ◽  
Heping Zhang ◽  
Xian׳an Jin ◽  
Wen-Yuan Qiu
Keyword(s):  
Polyhedral Links ◽  
Ear Decomposition

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 Space

2004 ◽  
pp. 226-226
Author(s):  
Steven Duplij ◽  
Steven Duplij ◽  
Steven Duplij
Keyword(s):  
Lens Space

scholarly journals $K$- and $KO$-rings of the lens space $L\spn(p\sp2)$ for odd prime $p$

1971 ◽  
Vol 1 (2) ◽  
pp. 273-286 ◽  
Author(s):  
Toshihisa Kawaguchi ◽  
Masahiro Sugawara
Keyword(s):  
Lens Space

scholarly journals Influence of scleral lenses on visual acuity and aberrations in patients with irregular cornea

The Eye ◽  
2019 ◽  
Vol 126 (2019-2) ◽  
pp. 32-39
Author(s):  
Olga Tikhonova ◽  
Nikolai Pashtaev ◽  
Nadezhda Pozdeyeva ◽  
Alexander Myagkov ◽  
Svetlana Bodrova ◽  
...  
Keyword(s):  
Visual Acuity ◽  
Laser Surgery ◽  
Contact Lenses ◽  
Lens Space ◽  
Astigmatism Correction ◽  
Intrastromal Corneal Ring ◽  
Stable Vision ◽  
Ring Segment ◽  
Ophthalmologic Examination ◽  
Fitting In

Purpose: To analyze changes of functional parame¬ters and aberrations before fitting and after using rigid gas-permeable scleral lenses (RGPSCL) in patients with irregular cornea. Material and methods. 21 patients (29 eyes) with irregular astigmatism of various etiology were enrolled in this study. The patients could not achieve good visual aсuity in glasses, standard soft or rigid corneal contact lenses. Complex ophthalmologic examination was per¬formed: autorefractometry, visometry, biomicroscopy, computer corneal topography, aberrometry on “OPD-Scan II” (“Nidek”, Japan) before fitting scleral lenses and during the period of their wearing. Results and discussion. The results demonstrat¬ed significant visual acuity improvement after RGP¬SCL fitting in all observed patients. UCVA amounted to 0.1±0.18, BCVA in glasses amounted to 0.4±0.26, BCVA in RGPSCL amounted to 0.7±0.1. An increase of best-corrected visual acuity in RGPSCL was statistically significant in patients after keratoplasty, after intra-stromal corneal ring segments (ICRS) implantation, af¬ter refractive laser surgery (RLS) and in cases of mixed astigmatism. We have found that the correction of ker¬atoconus with the use of RGPSCL resulted in a decrease of the root mean square value (RMS), measured in the 3 mm and 5 mm zones by 2.5 times and 4 times, re¬spectively. In patients wearing RGPSCL after kerato¬plasty, statistically significant decrease in RMS was observed in the 3 mm zone (by 3.85 times) and in the 5 mm zone (by 2.99 times). In patients wearing RGPSCL after implantation of intrastromal corneal ring segment (ICRS), RMS in the 3 mm zone decreased by 1.5 times. In patients wearing RGPSCL after refractive laser surgery (RLS) RMS was 2.5 times lower in the 3 mm zone and 2.8 times lower in the 5 mm zone. In case of mixed astigmatism correction with RGPSCL, RMS increased by 1.6 times in the 3 mm zone and practically did not change in the 5 mm zone. Conclusion. The results obtained demonstrated significant visual acuity improvement in all observed patients. The sub-lens-space filled with tear forms a unified “cornea-tear-scleral contact lens” optic system that corrects unevenness of cornea, decreases amount of high-order aberrations (HOA) and provides a clear stable vision.

scholarly journals On totally umbilicalCR-submanifolds of a Kaehler manifold

1993 ◽  
Vol 16 (2) ◽  
pp. 405-408
Author(s):  
M. A. Bashir
Keyword(s):  
Sectional Curvature ◽  
Mean Curvature ◽  
Curvature Vector ◽  
Lens Space ◽  
Holomorphic Sectional Curvature ◽  
Mean Curvature Vector ◽  
Kaehler Manifold ◽  
Totally Umbilical ◽  
The Mean

LetMbe a compact3-dimensional totally umbilicalCR-submanifold of a Kaehler manifold of positive holomorphic sectional curvature. We prove that if the length of the mean curvature vector ofMdoes not vanish, thenMis either diffeomorphic toS3orRP3or a lens spaceLp,q3.

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