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arXiv · 1909.01514

The Witt group of real surfaces

Max Karoubi·Charles Weibel
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Abstract

Let $V$ be an algebraic variety defined over $\mathbb R$, and $V_{top}$ the space of its complex points. We compare the algebraic Witt group $W(V)$ of symmetric bilinear forms on vector bundles over $V$, with the topological Witt group $WR(V_{top})$ of symmetric forms on Real vector bundles over $V_{top}$ in the sense of Atiyah, especially when $V$ is 2-dimensional. To do so, we develop topological tools to calculate $WR(V_{top})$, and to measure the difference between $W(V)$ and $WR(V_{top})$.

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Max Karoubi, Charles Weibel. 2019-09-04. The Witt group of real surfaces. https://arxiv.org/abs/1909.01514

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