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Journal of the London Mathematical Society 1986 s2-34(2):369-374; doi:10.1112/jlms/s2-34.2.369
© 1986 by London Mathematical Society
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© Oxford University Press

Finite Simple Even-Dimensional Knots

Jonathan A. Hillman

Department of Mathematics, Faculty of Science, Australian National University Canberra ACT 2601, Australia

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.

Current address: School of Mathematics and Physics, Macquarie University, North Ryde, New South Wales 2113, Australia


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