Reducing Spheres and Klein Bottles after Dehn Fillings

2003 ◽  
Vol 46 (2) ◽  
pp. 265-267 ◽  
Author(s):  
Seungsang Oh
Keyword(s):  
Short Proof ◽  
Klein Bottle ◽  
Dehn Fillings

AbstractLet M be a compact, connected, orientable, irreducible 3-manifold with a torus boundary. It is known that if two Dehn fillings on M along the boundary produce a reducible manifold and a manifold containing a Klein bottle, then the distance between the filling slopes is at most three. This paper gives a remarkably short proof of this result.

scholarly journals REDUCING DEHN FILLINGS AND SMALL SURFACES

2005 ◽  
Vol 92 (1) ◽  
pp. 203-223 ◽  
Author(s):  
SANGYOP LEE ◽  
SEUNGSANG OH ◽  
MASAKAZU TERAGAITO
Keyword(s):  
Projective Plane ◽  
Klein Bottle ◽  
Hyperbolic Manifolds ◽  
The Other ◽  
Möbius Band ◽  
Dehn Fillings ◽  
Orientable Surfaces

In this paper we investigate the distances between Dehn fillings on a hyperbolic 3-manifold that yield 3-manifolds containing essential small surfaces including non-orientable surfaces. In particular, we study the situations where one filling creates an essential sphere or projective plane, and the other creates an essential sphere, projective plane, annulus, Möbius band, torus or Klein bottle, for all eleven pairs of such non-hyperbolic manifolds.

Klein slopes on hyperbolic 3-manifolds

2007 ◽  
Vol 143 (2) ◽  
pp. 419-447
Author(s):  
DANIEL MATIGNON ◽  
NABIL SAYARI
Keyword(s):  
Upper Bound ◽  
Klein Bottle ◽  
Hyperbolic Manifolds ◽  
Dehn Fillings

AbstractThis paper is devoted to 3-manifolds which admit two distinct Dehn fillings producing a Klein bottle.LetMbe a compact, connected and orientable 3-manifold whose boundary contains a 2-torusT. IfMis hyperbolic then only finitely many Dehn fillings alongTyield non-hyperbolic manifolds. We consider the situation where two distinct slopes γ1, γ2produce a Klein bottle. We give an upper bound for the distance Δ(γ1, γ2), between γ1and γ2. We show that there are exactly four hyperbolic manifolds for which Δ(γ1, γ2) > 4.

scholarly journals DEHN FILLINGS CREATING ESSENTIAL SPHERES AND TORI

2002 ◽  
Vol 11 (06) ◽  
pp. 887-890
Author(s):  
SANGYOP LEE ◽  
SEUNGSANG OH ◽  
MASAKAZU TERAGAITO
Keyword(s):  
Boundary Component ◽  
Short Proof ◽  
Dehn Fillings

Let M be a simple 3-manifold with a toral boundary component. It is known that if two Dehn fillings on M along the boundary produce a reducible manifold and a toroidal mainfold, then the distance between the filling slopes is at most three. This paper gives a remarkably short proof of this result.

Dehn fillings of Klein bottle bundles

1992 ◽  
Vol 112 (2) ◽  
pp. 255-270 ◽  
Author(s):  
Wolfgang Heil ◽  
Pedja Raspopović
Keyword(s):  
Klein Bottle ◽  
Dehn Fillings

An important problem in the topology of 3-manifolds is to classify manifolds obtained by Dehn surgeries on a knot in a closed 3-manifold, or equivalently, Dehn fillings of a 3-manifold M with boundary a torus.

A note on generalized quasi-contraction

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3091-3093
Author(s):  
Dejan Ilic ◽  
Darko Kocev
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Short Proof

In this paper we give a short proof of the main results of Kumam, Dung and Sitthithakerngkiet (P. Kumam, N.V. Dung, K. Sitthithakerngkiet, A Generalization of Ciric Fixed Point Theorems, FILOMAT 29:7 (2015), 1549-1556).

Short proof that Kneser graphs are Hamiltonian for n ⩾ 4k

2021 ◽  
Vol 344 (7) ◽  
pp. 112430
Author(s):  
Johann Bellmann ◽  
Bjarne Schülke
Keyword(s):  
Short Proof ◽  
Kneser Graphs

scholarly journals Strongly perfect claw‐free graphs—A short proof

2021 ◽  
Author(s):  
Maria Chudnovsky ◽  
Cemil Dibek
Keyword(s):  
Short Proof

scholarly journals A short note on extreme points of certain polytopes

2020 ◽  
Vol 8 (1) ◽  
pp. 36-39
Author(s):  
Lei Cao ◽  
Ariana Hall ◽  
Selcuk Koyuncu
Keyword(s):  
Short Proof ◽  
Convex Polytopes ◽  
Short Note ◽  
Convex Polytope ◽  
Extreme Points ◽  
Alternative Proof ◽  
Stochastic Matrices ◽  
Doubly Stochastic ◽  
Birkhoff's Theorem ◽  
Birkhoff’S Theorem

AbstractWe give a short proof of Mirsky’s result regarding the extreme points of the convex polytope of doubly substochastic matrices via Birkhoff’s Theorem and the doubly stochastic completion of doubly sub-stochastic matrices. In addition, we give an alternative proof of the extreme points of the convex polytopes of symmetric doubly substochastic matrices via its corresponding loopy graphs.

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