The C₂-equivariant K (1) -local sphere

Key Points

• The research aims to compute the RO(C_2)-graded Green functor linked to the C_2-local sphere.
• Compute RO(C_2)-graded Green functor using K-theory
• Analyze L_{KU_{C_2}/(2)}S_{C_2} structure
• Apply equivariant stable homotopy techniques
• Explicit computation of the RO(C_2)-graded structure is achieved
• Establishes new connections in stable homotopy theory
• Provides insights into the C_2-local sphere properties