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Surgery Groups of Knot and Link Complements
Author(s) -
Aravinda C. S.,
Farrell F. T.,
Roushon S. K.
Publication year - 1997
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609396002846
Subject(s) - mathematics , knot (papermaking) , homomorphism , combinatorics , mathematics subject classification , homotopy , isomorphism (crystallography) , equivalence (formal languages) , knot invariant , conjecture , pure mathematics , knot theory , algebra over a field , crystallography , crystal structure , chemistry , chemical engineering , engineering
Cappell conjectured the following in [ 2 ]; compare [ 11 , Problem 2]. Conjecture 0.1. Let π be the fundamental group of a knot complement in S 3 . ThenL n h ( π ) ≃ L n h ( Z )for all n, whereL n his the Wall–Novikov surgery group for homotopy equivalence, and the isomorphism is induced from the abelianization homomorphism π→ℤ. 1991 Mathematics Subject Classification 19D35, 19D50, 57N37, 57R69.