The 2-local homotopy types of G_2-gauge groups
We determine the 2-local homotopy types of G_2-gauge groups over S^4.
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arXiv subjects
Masaki Kameko
Publications and source records attributed to Masaki Kameko.
Coniveau filtrations with Z/2 coefficients
We show that two coniveau filtrations on the mod 2 cohomology group of a smooth projective complex variety differ.
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Torsion in classifying spaces of gauge groups
We determine when the integral homology of the classifying space of a PU(n)-gauge group over the sphere S^2 has torsion.
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Milnor operations and classifying spaces
We give an example of a nonzero odd degree element of the classifying space of a connected Lie group such that all higher Milnor operations vanish on it. It is a counterexample for a conjecture of Kono and Yagita.
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Nilpotent elements in the cohomology of the classifying space of a connected Lie group
We give an example of a compact connected Lie group of the lowest rank such that the mod 2 cohomology ring of its classifying space has a nonzero nilpotent element.
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Homotopy types of gauge groups over Riemann surfaces
Let $G$ be a compact connected Lie group with $π_1(G)\cong\mathbb{Z}$. We study the homotopy types of gauge groups of principal $G$-bundles over Riemann surfaces. This can be applied to an explicit computation of the homotopy groups of the moduli spaces of stable vector bundles over Riemann surfaces.
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Non-torsion non-algebraic classes in the Brown-Peterson tower
Generalizing the classical work of Atiyah and Hirzebruch on non-algebraic classes, recently Quick proved the existence of torsion non-algebraic elements in the Brown-Peterson tower. We construct non-torsion non-algebraic elements in the Brown-Peterson tower for the prime number 2.
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On the motivic Peterson conjecture
We show that the analogue of the Peterson conjecture on the action of Steenrod squares does not hold in motivic cohomology.
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Representation theory and the cycle map of a classifying space
We compute the Chern subgroup of the 4-th integral cohomology group of a certain classifying space and show that it is a proper subgroup. Such a classifying space gives us new counterexamples for the integral Hodge and Tate conjectures modulo torsion.
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Mod 3 Chern classes and generators
We show the non-triviality of the mod 3 Chern class of degree 324 of the adjoint representation of the exceptional Lie group E_8.
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On the cycle map of a finite group
Let p be an odd prime number. We show that there exists a finite group of order p^{p+3} whose the mod p cycle map from the mod p Chow ring of its classifying space to its ordinary mod p cohomology is not injective.
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On the integral Tate conjecture for finite fields
We give non-torsion counterexamples against the integral Tate conjecture for finite fields. We extend the result due to Pirutka and Yagita for prime numbers 2,3,5 to all prime numbers.
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Cohomology of classifying spaces of loop groups and finite Chevalley groups associated with spin groups
For n>2, we prove the mod 2 cohomology of the finite Chevalley group Spin_n(F_q) is isomorphic to that of the classifying space of the loop group of the spin group Spin(n).
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Weyl group invariants
For any odd prime $p$, we prove that the induced homomorphism from the mod $p$ cohomology of the classifying space of a compact simply-connected simple connected Lie group to the Weyl group invariants of the mod $p$ cohomology of the classifying space of its maximal torus is an epimorphism except for the case $p=3$, $G=E_8$.
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Chern classes and generators
We give a simple proof for the fact that algebra generators of the mod 2 cohomology of classifying spaces of exceptional Lie groups are given by Chern classes and Stiefel-Whitney classes of certain representations.
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On the Rothenberg-Steenrod spectral sequence for the mod 2 cohomology of classifying spaces of spinor groups
We compute the cotorsion product of the mod 2 cohomology of spinor group spin(n), which is the E_2-term of the Rothenberg-Steenrod spectral sequence for the mod 2 cohomology of the classifying space of the spinor group spin(n). As a consequence of this computation, we show the non-collapsing of the Rothenberg-Steenrod spectral sequence for n > 16.
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Mui invariants and Milnor operations
We describe Mui invariants in terms of Milnor operations and give a simple proof for Mui's theorem on rings of invariants of polynomial tensor exterior algebras with respect to the action of finite general linear groups. Moreover, we compute some rings of invariants of Weyl groups of maximal non-toral elementary abelian p-subgroups of exceptional Lie groups.
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On the Rothenberg-Steenrod spectral sequence for the mod 3 cohomology of the classifying space of the exceptional Lie group E_8
We show that the Rothenberg--Steenrod spectral sequence converging to the mod 3 cohomology of the classifying space of the exceptional Lie group E_8 does not collapse at the E_2-level.
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