Squaring operations in the $RO(C_2)$-graded and real motivic Adams spectral sequences

Abstract

In this paper we establish a formula for computing $d_2(s{q}^i(x))$ where $x$ is a permanent cycle in the $C_2$-equivariant Adams spectral sequence or the motivic Adams spectral sequence over $Spec(\mathbb{R})$. This requires establishing that the Adams towers have an $H_{\infty }$-structure as well as determining the attaching maps for $C_2$-equivariant projective spaces. The attaching maps of $C_2$-equivariant projective spaces can then be used to determine the coefficients of differentials in both the equivariant and motivic case. At the end some sample computations are given.

Results extended from previous version to cover the real motivic Adams spectral sequence

References in corpus (1)

• From algebraic cobordism to motivic cohomology