Irreducibility and knot surgery

2014 ◽  
Vol 46 (3) ◽  
pp. 571-575
Author(s):  
B. Doug Park
Keyword(s):  
Knot Surgery

scholarly journals Fintushel-Stern knot surgery in torus bundles

2017 ◽  
Vol 10 (1) ◽  
pp. 164-177
Author(s):  
Yi Ni
Keyword(s):  
Torus Bundles ◽  
Knot Surgery

Knot surgery and primeness

1986 ◽  
Vol 99 (1) ◽  
pp. 89-102 ◽  
Author(s):  
Francisco González Acuña ◽  
Hamish Short
Keyword(s):  
Dehn Surgery ◽  
Connected Sum ◽  
Low Dimensional Topology ◽  
Knot Surgery ◽  
Low Dimensional ◽  
Image Position

The aim of this paper is to prove some new results towards answering the question: When does Dehn surgery on a knot give a non-prime manifold? This question has been raised on several occasions (see for instance [5] or [4]; concerning the latter see below). Recall that a 3-manifold is prime if, in any connected sum decompositionone of M1, M2 is S3. (For standard definitions of low-dimensional topology see [2] or [16].)

scholarly journals Homology handles with multiple knot-surgery descriptions

1994 ◽  
Vol 56 (3) ◽  
pp. 249-257 ◽  
Author(s):  
Masakazu Teragaito
Keyword(s):  
Knot Surgery

ON THE DIFFEOMORPHISMS FOR AKBULUT'S KNOT CONCORDANCE SURGERY

2005 ◽  
Vol 14 (05) ◽  
pp. 539-563
Author(s):  
MOTOO TANGE
Keyword(s):  
Knot Concordance ◽  
Trefoil Knot ◽  
Knot Surgery

Akbulut generalized Fintushel–Stern knot surgery in a certain way. He showed that an operation C(K#(-K)) → { diffeo type of X} is not injective, where C(K#(-K)) is self-concordance set of K#(-K) and K is trefoil knot. In the present paper we prove that the same phenomenon occurs for any knot K and for some other knots L instead of K#(-K).

Manifolds with multiple knot-surgery descriptions

1980 ◽  
Vol 87 (3) ◽  
pp. 443-448 ◽  
Author(s):  
W. R. Brakes
Keyword(s):  
Three Sphere ◽  
Knot Surgery ◽  
Link Surgery

Every closed connected orientable three-manifold can be constructed by surgery along an appropriately chosen link in the three-sphere, S3 ((10), (15)). Such a link-surgery description is never unique, but the equivalence between different descriptions has been explicitly identified ((8),(3)). However, the situation with regard to manifolds that can be obtained by surgery along a knot in S3 is less clear ((6), p. 47): some manifolds are known to have at least two knot-surgery descriptions ((12), (14), p. 270, (1), (11)), whilst certain manifolds (e.g. S3 and S2 × S1) are widely suspected to have just one (see problems 1·15, 1·16 of (9)).

scholarly journals DOUBLE KNOT SURGERIES TO S4 AND S2 × S2

2011 ◽  
Vol 22 (12) ◽  
pp. 1735-1741 ◽  
Author(s):  
SELMAN AKBULUT
Keyword(s):  
Diffeomorphism Type ◽  
Knot Surgery

It is known that S4 is a union of two fishtails, and S2 × S2 is a union of two cusps (glued along their boundaries). Here we prove that for any choice of knots K, L ⊂ S3 the knot surgery operations [Formula: see text] and S2 × S2 ⇝ (S2 × S2)K, L along both of these fishtails and cusps, respectively, do not change the diffeomorphism type of these manifolds.

Nonisomorphic Lefschetz fibrations on knot surgery 4-manifolds

2009 ◽  
Vol 345 (3) ◽  
pp. 581-597 ◽  
Author(s):  
Jongil Park ◽  
Ki-Heon Yun
Keyword(s):  
Lefschetz Fibrations ◽  
Knot Surgery
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