Matches in SemOpenAlex for { <https://semopenalex.org/work/W2103057558> ?p ?o ?g. }
Showing items 1 to 60 of
60
with 100 items per page.
- W2103057558 endingPage "186" @default.
- W2103057558 startingPage "153" @default.
- W2103057558 abstract "A nontrivial knot that can be drawn with only two relative maxima in the vertical direction is called a 2-bridge knot, and one that can be drawn on a torus is called a torus knot. Loosely speaking, a lamination in a manifold M is a foliation of M, except that it can have a nonempty open complement in M, and very loosely speaking, the lamination is essential if each leaf of it L is incompressible, i.e. inclusion of L into M induces an injective homomorphism from 1(L) into 1(M). Our main result is: Theorem 2. Every 3-manifold obtained by surgery on a nontorus 2-bridge knot admits essential laminations. Some immediate corollaries are that these manifolds are covered by R 3 , and have innite fundamental group. So Property P is true for non-torus 2-bridge knots, i.e. surgery on these knots never yields a homotopy 3-sphere, or a counterexample to the Poincare conjecture. We use general techniques which are not specic to 2-bridge knots to nd and explicitly construct these laminations. In trying to understand 3-manifolds with the hope of eventually classifying them, as with 2-manifolds, one approach that has turned out to be fruitful is to study objects of codimension one in them, more specically, incompressible surfaces, Reebless foliations, and essential laminations. For a 3-manifoldM containing an incompressible surface, with some extra hypotheses, Waldhausen proved: The universal cover of M is R 3 , the topology of M is determined by its fundamental group, and homotopic homeomorphisms of M are isotopic. Similar theorems for manifolds containing Reebless foliations were proven by Haefliger, Novikov, Palmeira, Rosenberg, and others. The essential lamination was developed in the 1980’s as a generalization of the incompressible surface and the Reebless foliation, which themselves qualify as essential laminations. In fact they are just extreme cases of essential laminations: At one end we have compact properly embedded surfaces," @default.
- W2103057558 created "2016-06-24" @default.
- W2103057558 creator A5018940157 @default.
- W2103057558 date "1997-09-01" @default.
- W2103057558 modified "2023-10-17" @default.
- W2103057558 title "Constructing essential laminations in 2-bridge knot surgered 3-manifolds" @default.
- W2103057558 cites W1964046881 @default.
- W2103057558 cites W1980585398 @default.
- W2103057558 cites W1997478387 @default.
- W2103057558 cites W2016828384 @default.
- W2103057558 cites W2046023199 @default.
- W2103057558 cites W2046756141 @default.
- W2103057558 cites W2075814994 @default.
- W2103057558 cites W2093914711 @default.
- W2103057558 cites W2315309061 @default.
- W2103057558 cites W2317004642 @default.
- W2103057558 cites W4250413898 @default.
- W2103057558 doi "https://doi.org/10.2140/pjm.1997.180.153" @default.
- W2103057558 hasPublicationYear "1997" @default.
- W2103057558 type Work @default.
- W2103057558 sameAs 2103057558 @default.
- W2103057558 citedByCount "8" @default.
- W2103057558 countsByYear W21030575582020 @default.
- W2103057558 crossrefType "journal-article" @default.
- W2103057558 hasAuthorship W2103057558A5018940157 @default.
- W2103057558 hasConcept C114614502 @default.
- W2103057558 hasConcept C159985019 @default.
- W2103057558 hasConcept C192562407 @default.
- W2103057558 hasConcept C202444582 @default.
- W2103057558 hasConcept C2524010 @default.
- W2103057558 hasConcept C2779863119 @default.
- W2103057558 hasConcept C33923547 @default.
- W2103057558 hasConceptScore W2103057558C114614502 @default.
- W2103057558 hasConceptScore W2103057558C159985019 @default.
- W2103057558 hasConceptScore W2103057558C192562407 @default.
- W2103057558 hasConceptScore W2103057558C202444582 @default.
- W2103057558 hasConceptScore W2103057558C2524010 @default.
- W2103057558 hasConceptScore W2103057558C2779863119 @default.
- W2103057558 hasConceptScore W2103057558C33923547 @default.
- W2103057558 hasIssue "1" @default.
- W2103057558 hasLocation W21030575581 @default.
- W2103057558 hasOpenAccess W2103057558 @default.
- W2103057558 hasPrimaryLocation W21030575581 @default.
- W2103057558 hasRelatedWork W1978042415 @default.
- W2103057558 hasRelatedWork W2017331178 @default.
- W2103057558 hasRelatedWork W2017419110 @default.
- W2103057558 hasRelatedWork W2035156587 @default.
- W2103057558 hasRelatedWork W2976797620 @default.
- W2103057558 hasRelatedWork W3011702906 @default.
- W2103057558 hasRelatedWork W3086542228 @default.
- W2103057558 hasRelatedWork W3106133691 @default.
- W2103057558 hasRelatedWork W4235281909 @default.
- W2103057558 hasRelatedWork W4245585316 @default.
- W2103057558 hasVolume "180" @default.
- W2103057558 isParatext "false" @default.
- W2103057558 isRetracted "false" @default.
- W2103057558 magId "2103057558" @default.
- W2103057558 workType "article" @default.