Sean Tilson
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The homology of connective Morava $E$-theory with coefficients in $\mathbb{F}_p$ Open
Let $e_n$ be the connective cover of the Morava $E$-theory spectrum $E_n$ of height $n$. In this paper we compute its homology $H_*(e_n;\mathbb{F}_p)$ for any prime $p$ and $n \leq 4$ up to possible multiplicative extensions. In order to a…
An algebraic $C_2$-equivariant Bézout's theorem Open
Bézout's theorem, nonequivariantly, can be interpreted as a calculation of the Euler class of a sum of line bundles over complex projective space, expressing it in terms of the rank of the bundle and its degree. We give here a generalizati…
A-module extensions Open
Explicit extensions representing cocycles $x \in Ext_{A}^{s,t}(F_2,F_2)$ are useful in calculating Steenrod operations $Sq^i : Ext_{A}^{s,t}(F_2,F_2) \longrightarrow Ext_{A}^{s+i,2t}(F_2,F_2)$ by a method devised by the second author. This…
Steenrod operations and A-module extensions Open
Explicit extensions representing cocycles $x \in Ext_{A}^{s,t}(F_2,F_2)$ are useful in calculating Steenrod operations $Sq^i : Ext_{A}^{s,t}(F_2,F_2) \longrightarrow Ext_{A}^{s+i,2t}(F_2,F_2)$ by a method devised by the second author. This…
The $\mathbb{Z}/2$-equivariant cohomology of complex projective spaces Open
In this article we compute the cohomology of complex projective spaces associated to finite dimensional representations of $\mathbb{Z}/2$ graded on virtual representations of its fundamental groupoid. This fully graded theory, unlike the c…
View article: The Homology of Connective Morava $E$-theory with coefficients in $\mathbb{F}_p$
The Homology of Connective Morava $E$-theory with coefficients in $\mathbb{F}_p$ Open
Let $e_n$ be the connective cover of the Morava $E$-theory spectrum $E_n$ of height $n$. In this paper we compute its homology $H_*(e_n;\mathbb{F}_p)$ for any prime $p$ and $n \leq 4$ up to possible multiplicative extensions. In order to a…
Squaring operations in the $RO(C_2)$-graded and real motivic Adams spectral sequences Open
In this paper we establish a formula for computing $d_2(sq^i(x))$ 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 th…
Power operations in the Kunneth spectral sequence and commutative HFp-algebras Open
In this paper, we prove the multiplicativity of the Künneth spectral sequence. This is established by an analogue of the Comparison Theorem from homological algebra, which we suspect may be useful for other spectral sequences. This multipl…