Witt classes of integral representations of an abelian 2-group

Gibbs, David E.

doi:10.1090/S0002-9939-1978-0492055-1

Witt classes of integral representations of an abelian $2$-group
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Proc. Amer. Math. Soc. 70 (1978), 103-108 Request permission

Abstract:

In this paper the Witt groups of integral representations of an abelian 2-group $\pi ,{W_0}(\pi ;Z)$ and ${W_2}(\pi ;Z)$ are calculated. Invariants are listed which completely determine ${W_0}({Z_4};Z)$ and ${W_2}({Z_4};Z)$ and can be extended to the case $\pi = {Z_{{2^k}}}$. If $\pi$ is an elementary abelian 2-group, it is shown that ${W_2}(\pi ;Z) = 0$ and ${W_0}(\pi ;Z[\tfrac {1}{2}])$ is ring isomorphic to the group ring $W(Z[\tfrac {1}{2}])({\operatorname {Hom}}(\pi ,{Z_2}))$.

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Corps locaux

Neal W. Stoltzfus, Unraveling the integral knot concordance group, Mem. Amer. Math. Soc. 12 (1977), no. 192, iv+91. MR 467764, DOI 10.1090/memo/0192