<p>We compute the <InlineEquation ID="IEq4"> <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 Green functor <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\underline{\pi }_\star L_{KU_{C_2}/(2)}S_{C_2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <munder> <mi>π</mi> <mo>̲</mo> </munder> <mo>⋆</mo> </msub> <msub> <mi>L</mi> <mrow> <mi>K</mi> <msub> <mi>U</mi> <msub> <mi>C</mi> <mn>2</mn> </msub> </msub> <mo stretchy="false">/</mo> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </msub> <msub> <mi>S</mi> <msub> <mi>C</mi> <mn>2</mn> </msub> </msub> </mrow> </math></EquationSource> </InlineEquation>.</p>

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The \(C_2\)-equivariant K(1)-local sphere

  • William Balderrama

摘要

We compute the \(RO(C_2)\) R O ( C 2 ) -graded Green functor \(\underline{\pi }_\star L_{KU_{C_2}/(2)}S_{C_2}\) π ̲ L K U C 2 / ( 2 ) S C 2 .