<p>We describe the main properties of the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$RO(C_2\times \Sigma _2)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mi>O</mi> <mo stretchy="false">(</mo> <msub> <mi>C</mi> <mn>2</mn> </msub> <mo>×</mo> <msub> <mi mathvariant="normal">Σ</mi> <mn>2</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-graded cohomology ring of a point and apply the results to compute the subring of motivic classes given by the Bredon motivic cohomology of real numbers and to compute <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$RO(C_2\times \Sigma _2)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mi>O</mi> <mo stretchy="false">(</mo> <msub> <mi>C</mi> <mn>2</mn> </msub> <mo>×</mo> <msub> <mi mathvariant="normal">Σ</mi> <mn>2</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-graded cohomology ring of <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$E_{\Sigma _2}C_2$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>E</mi> <msub> <mi mathvariant="normal">Σ</mi> <mn>2</mn> </msub> </msub> <msub> <mi>C</mi> <mn>2</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>. This generalizes Voevodsky’s identification of motivic cohomology of real numbers with the positive cone of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$RO(C_2)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>R</mi> <mi>O</mi> <mo stretchy="false">(</mo> <msub> <mi>C</mi> <mn>2</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> graded cohomology of a point.</p>

$RO(C_2\times C_2)$-graded cohomology ring of a point and applications

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2026年6月24日

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Bill Deng,
Mircea Voineagu

摘要

We describe the main properties of the $RO(C_2\times \Sigma _2)$ $R O (C_{2} \times Σ_{2})$ -graded cohomology ring of a point and apply the results to compute the subring of motivic classes given by the Bredon motivic cohomology of real numbers and to compute $RO(C_2\times \Sigma _2)$ $R O (C_{2} \times Σ_{2})$ -graded cohomology ring of $E_{\Sigma _2}C_2$ $E_{Σ_{2}} C_{2}$ . This generalizes Voevodsky’s identification of motivic cohomology of real numbers with the positive cone of $RO(C_2)$ $R O (C_{2})$ graded cohomology of a point.

\(RO(C_2\times C_2)\)-graded cohomology ring of a point and applications

摘要