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Finite Simple Even‐Dimensional Knots
Author(s) -
Hillman Jonathan A.
Publication year - 1986
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-34.2.369
Subject(s) - mathematics , functor , knot (papermaking) , simple (philosophy) , pure mathematics , knot theory , duality (order theory) , simple group , combinatorics , algebra over a field , chemical engineering , engineering , philosophy , epistemology
We reformulate Farber's invariants for simple even‐dimensional knots in the finite case as the self dual objects of an additive category with duality functor; we apply the work of Quebbemann, Scharlau and Schulte to show that the semigroup of such knots is almost free, and that the fourfold connected sum of such a knot with itself is doubly null concordant. In fact the Witt group arising from the algebra is a sum of infinitely many copies of Z/2Z and of Z/4Z.
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