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Talk:Arf-invariant

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Definition and existence

The presentation in this article seems odd. We start with a -module with a symplectic form \psi and then assume (explicitly) that there is a \psi_0 which is a quadratic form on L \otimes \mathbf{Z}/2\mathbf{Z}, and then assume (implicitly) that any such \psi_0, should any exist, gives a consistent value of \mathrm{Arf}.

It would make more sense to start with \psi_0 a quadratic form on a module over a field k of characteristic two, define \psi(x,y) by polarisation \psi_0(x+y) - \psi_0(x) - \psi_0(y), define \mathrm{Arf} with respect to some symplectic basis, and then assert that it is independent of choice of basis. This seems to be the more usual presentation. Richard Pinch (talk) 20:45, 24 December 2017 (CET)

How to Cite This Entry:
Arf-invariant. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Arf-invariant&oldid=42587