Igor Kříž
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View article: Equivariant operations in topological Hochschild homology
Equivariant operations in topological Hochschild homology Open
We observe a new equivariant relationship between topological Hochschild homology and cohomology. We also calculate the topological Hochschild homology of the topological Hochschild cohomology of a finite prime field, which can be viewed a…
View article: The $\mathbb{Z}/p$-equivariant spectrum $BP\mathbb{R}$ for an odd prime $p$
The $\mathbb{Z}/p$-equivariant spectrum $BP\mathbb{R}$ for an odd prime $p$ Open
In the present paper, we construct a $\mathbb{Z}/p$-equivariant analog of the $\mathbb{Z}/2$-equivariant spectrum $BP\mathbb{R}$ previously constructed by Hu and Kriz. We prove that this spectrum has some of the properties conjectured by H…
View article: Stable equivariant complex cobordism of the symmetric group on three elements
Stable equivariant complex cobordism of the symmetric group on three elements Open
In this paper, we calculate the coefficient ring of equivariant Thom complex cobordism for the symmetric group on three elements.We also make some remarks on general methods of calculating certain pullbacks of rings which typically occur i…
View article: On the equivariant motivic filtration of the topological Hochschild homology of polynomial algebras
On the equivariant motivic filtration of the topological Hochschild homology of polynomial algebras Open
We identify the equivariant structure of the filtered pieces of the motivic filtration defined by Bhatt, Morrow and Scholze on the topological Hochschild cohomology spectrum of polynomial algebras over $\mathbb{F}_p$.
View article: The $\mathbb{Z}/p$-equivariant dual Steenrod algebra for an odd prime $p$
The $\mathbb{Z}/p$-equivariant dual Steenrod algebra for an odd prime $p$ Open
We completely calculate the $RO(\mathbb{Z}/p)$-graded coefficients $H\underline{\mathbb{Z}/p}_\star H\underline{\mathbb{Z}/p}$ for the constant Mackey functor $\underline{\mathbb{Z}/p}$.
View article: Coefficients of the $Σ_3$-equivariant complex cobordism ring
Coefficients of the $Σ_3$-equivariant complex cobordism ring Open
In this paper, we calculate the coefficient ring of equivariant Thom complex cobordism for the symmetric group on three elements. We also make some remarks on general methods of calculating certain pullbacks of rings which typically occur …
View article: Coefficients of the $\Sigma_3$-equivariant complex cobordism ring
Coefficients of the $\Sigma_3$-equivariant complex cobordism ring Open
In this paper, we calculate the coefficient ring of equivariant Thom complex\ncobordism for the symmetric group on three elements. We also make some remarks\non general methods of calculating certain pullbacks of rings which typically\nocc…
View article: Equivariant formal group laws and complex-oriented spectra over primary cyclic groups: Elliptic curves, Barsotti-Tate groups, and other examples
Equivariant formal group laws and complex-oriented spectra over primary cyclic groups: Elliptic curves, Barsotti-Tate groups, and other examples Open
We explicitly construct and investigate a number of examples of $\mathbb{Z}/p^r$-equivariant formal group laws and complex-oriented spectra, including those coming from elliptic curves and $p$-divisible groups, as well as some other relate…
View article: On the $RO(G)$-graded coefficients of dihedral equivariant cohomology
On the $RO(G)$-graded coefficients of dihedral equivariant cohomology Open
We completely calculate the $RO(G)$-graded coefficients of ordinary equivariant cohomology where $G$ is the dihedral group of order $2p$ for a prime $p>2$ both with constant and Burnside ring coefficients. The authors first proved it for $…
View article: On the Coefficients of $(\mathbb{Z}/p)^n$-Equivariant Ordinary Cohomology with Coefficients in $\mathbb{Z}/p$
On the Coefficients of $(\mathbb{Z}/p)^n$-Equivariant Ordinary Cohomology with Coefficients in $\mathbb{Z}/p$ Open
This note contains a generalization to $p>2$ of the authors' previous calculations of the coefficients of $(\mathbb{Z}/2)^n$-equivariant ordinary cohomology with coefficients in the constant $\mathbb{Z}/2$-Mackey functor. The algberaic res…
View article: Tate cohomology of connected k-theory for elementary abelian groups revisited
Tate cohomology of connected k-theory for elementary abelian groups revisited Open
Tate cohomology (as well as Borel homology and cohomology) of connective K-theory for $G=(\mathbb{Z}/2)^n$ was completely calculated by Bruner and Greenlees. In this note, we essentially redo the calculation by a different, more elementary…
View article: Derived representation theory of Lie algebras and stable homotopy categorification of $sl_k$
Derived representation theory of Lie algebras and stable homotopy categorification of $sl_k$ Open
We set up foundations of representation theory over $S$, the sphere spectrum, which is the `initial ring' of stable homotopy theory. In particular, we treat $S$-Lie algebras and their representations, characters, $gl_n(S)$-Verma modules an…
View article: On the definition and K-theory realization of a modular functor
On the definition and K-theory realization of a modular functor Open
We present a definition of a (super)-modular functor which includes certain interesting cases that previous definitions do not allow. We also introduce a notion of topological twisting of a modular functor, and construct formally a realiza…
View article: Kan's combinatorial spectra and their sheaves revisited
Kan's combinatorial spectra and their sheaves revisited Open
We define a right Cartan-Eilenberg structure on the category of Kan's combinatorial spectra, and the category of sheaves of such spectra, assuming some conditions. In both structures, we use the geometric concept of homotopy equivalence as…
View article: Kan's combinatorial spectra and their sheaves revisited
Kan's combinatorial spectra and their sheaves revisited Open
We define a right Cartan-Eilenberg structure on the category of Kan's combinatorial spectra, and the category of sheaves of such spectra, assuming some conditions. In both structures, we use the geometric concept of homotopy equivalence as…
View article: Some non-trivial examples of the Baldwin-Ozsváth-Szabó twisted spectral sequence and Heegaard-Floer homology of branched double covers
Some non-trivial examples of the Baldwin-Ozsváth-Szabó twisted spectral sequence and Heegaard-Floer homology of branched double covers Open
We present some non-trivial calculations of Baldwin-Ozsváth-Szabó cohomology of links, and applications to Heegaard-Floer homology of branched double covers.
View article: The equivariant complex cobordism ring of a finite abelian group
The equivariant complex cobordism ring of a finite abelian group Open
We compute the equivariant (stable) complex cobordism ring $(MU_G)_*$ for finite abelian groups $G$.
View article: The equivariant complex cobordism ring of a finite abelian group
The equivariant complex cobordism ring of a finite abelian group Open
We compute the equivariant (stable) complex cobordism ring (MUG)∗ for finite abelian groups G.