The knot cobordism groups

Abstract

The cobordism groups C _n of n-knots k : S ⁿ ⊂ S ⁿ⁺² were first defined in the 1960’s. The computation in the high dimensions n ≥ 3 was completed by the 1970’s. The object of this final chapter is to give a brief description of the algebraic structure of the odd-dimensional groups

$${C_{2j - 1}} = \widehat {{L_0}}({\Bbb Z},{( - )^j}) = LIs{o^0}({\Bbb Z},{( - )^j})$$

$$LAs{y^0}({\Bbb Z},P,{( - )^j}) = {L_0}({\Bbb Z}[z,{z^{ - 1}}],P,{( - )^{j + 1}})(j2)$$

with $P = \left\{ {p(z)\left| {p(1) = \pm 1} \right.} \right\} \subset {\Bbb Z}\left[ {z,{z^{ - 1}}} \right]$