Masaki Kameko

THE BROWN-PETERSON COHOMOLOGY OF THE CLASSIFYING SPACES OF THE PROJECTIVE UNITARY GROUPS PU(p) AND EXCEPTIONAL LIE GROUPS

For a fixed prime p, we compute the Brown-Peterson cohomologies of classifying spaces of PU(p) and exceptional Lie groups by using the Adams spectral sequence. In particular, we see that BP*(BPU(p)) and K(n)*(BPU(p)) are even dimensionally generated.

Representation theory and the cycle class 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.

Mùi invariants and Milnor operations

We describe Mui invariants in terms of Milnor operations and give a simple proof for Muis 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.

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.

On the integral Tate conjecture over 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.

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.

Coniveau spectral sequences of classifying spaces for exceptional and Spin groups

Let k be an algebraically closed field of ch ( k ) = 0 and G be a simple simply connected algebraic group G over k . By using results about cohomological invariants, we compute the coniveau spectral sequence for classifying spaces BG .

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.

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.

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.