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• W3100761937 abstract "Let $V$ be an algebraic variety over $mathbb R$. The purpose of this paper is to compare its algebraic Witt group $W(V)$ with a new topological invariant $WR(V_{mathbb C})$, based on symmetric forms on Real vector bundles (in the sense of Atiyah) on the space of complex points of $V$, This invariant lies between $W(V)$ and the group $KO(V_{mathbb R})$ of $mathbb R$-linear topological vector bundles on $V_{mathbb R}$, the set of real points of $V$. We show that the comparison maps $W(V)to WR(V_{mathbb C})$ and $WR(V_{mathbb C})to KO(V_{mathbb R})$ that we define are isomorphisms modulo bounded 2-primary torsion. We give precise bounds for the exponent of the kernel and cokernel of these maps, depending upon the dimension of $V.$ These results improve theorems of Knebusch, Brumfiel and Mah'e. Along the way, we prove a comparison theorem between algebraic and topological Hermitian $K$-theory, and homotopy fixed point theorems for the latter. We also give a new proof (and a generalization) of a theorem of Brumfiel." @default.
• W3100761937 created "2020-11-23" @default.
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• W3100761937 date "2016-11-03" @default.
• W3100761937 modified "2023-10-14" @default.
• W3100761937 title "The Witt group of real algebraic varieties" @default.
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• W3100761937 doi "https://doi.org/10.1112/jtopol/jtw024" @default.
• W3100761937 hasPublicationYear "2016" @default.
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