# Talk:Arf-invariant

## Definition and existence

The presentation in this article seems odd. We start with a $\mathbf{Z}$-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