Expand all Collapse all | Results 26 - 33 of 33 |
26. CMB 1999 (vol 42 pp. 129)
Hecke Operations and the Adams $E_2$-Term Based on Elliptic Cohomology Hecke operators are used to investigate part of the $\E_2$-term of
the Adams spectral sequence based on elliptic homology. The main
result is a derivation of $\Ext^1$ which combines use of classical
Hecke operators and $p$-adic Hecke operators due to Serre.
Keywords:Adams spectral sequence, elliptic cohomology, Hecke operators Categories:55N20, 55N22, 55T15, 11F11, 11F25 |
27. CMB 1999 (vol 42 pp. 248)
The Classification of $\Pin_4$-Bundles over a $4$-Complex In this paper we show that the Lie-group $\Pin_4$ is isomorphic to
the semidirect product $(\SU_2\times \SU_2)\timesv \Z/2$ where
$\Z/2$ operates by flipping the factors. Using this structure
theorem we prove a classification theorem for $\Pin_4$-bundles over
a finite $4$-complex $X$.
Categories:55N25, 55R10, 57S15 |
28. CMB 1999 (vol 42 pp. 52)
Embedding Coverings in Bundles If $V\to X$ is a vector bundle of fiber dimension $k$ and $Y\to X$
is a finite sheeted covering map of degree $d$, the implications
for the Euler class $e(V)$ in $H^k(X)$ of $V$ implied by the
existence of an embedding $Y\to V$ lifting the covering map are
explored. In particular it is proved that $dd'e(V)=0$ where $d'$
is a certain divisor of $d-1$, and often $d'=1$.
Categories:57M10, 55R25, 55S40, 57N35 |
29. CMB 1998 (vol 41 pp. 20)
A new cohomological criterion for the $p$-nilpotence of groups Let $G$ be a finite group, $H$ a copy of its $p$-Sylow
subgroup, and $\kn$ the $n$-th Morava $K$-theory at $p$.
In this paper we prove that the existence of an
isomorphism between $K(n)^\ast(BG)$ and $K(n)^\ast(BH)$ is
a sufficient condition for $G$ to be $p$-nilpotent.
Categories:55N20, 55N22 |
30. CMB 1998 (vol 41 pp. 28)
Gorenstein graded algebras and the evaluation map We consider graded connected Gorenstein algebras with respect
to the evaluation map $\ev_G = \Ext_G(k,\varepsilon )=::
\Ext_G(k,G) \longrightarrow \Ext_G(k,k)$. We prove that if
$\ev_G \neq 0$, then the global dimension of $G$ is finite.
Categories:55P35, 13C11 |
31. CMB 1997 (vol 40 pp. 341)
The stable and unstable types of classifying spaces The main purpose of this paper is to study groups $G_1$, $G_2$ such that
$H^\ast(BG_1,{\bf Z}/p)$ is isomorphic to $H^\ast(BG_2,{\bf Z}/p)$
in ${\cal U}$, the category of unstable modules over the Steenrod algebra
${\cal A}$, but not isomorphic as graded algebras over ${\bf Z}/p$.
Categories:55R35, 20J06 |
32. CMB 1997 (vol 40 pp. 193)
Finite rank operators and functional calculus on Hilbert modules over abelian $C^{\ast}$-algebras We consider the problem: If $K$ is a compact normal operator on a Hilbert
module $E$, and $f\in C_0(\Sp K)$ is a function which is zero in a
neighbourhood of the origin, is $f(K)$ of finite rank? We show that
this is the case if the underlying $C^{\ast}$-algebra is abelian, and that
the range of $f(K)$ is contained in a finitely generated projective
submodule of $E$.
Categories:55R50, 47A60, 47B38 |
33. CMB 1997 (vol 40 pp. 108)
Continuous Self-maps of the Circle Given a continuous map $\delta$ from the circle $S$ to itself we
want to find all self-maps $\sigma\colon S\to S$ for which
$\delta\circ\sigma = \delta$. If the degree $r$ of $\delta$ is not
zero, the transformations $\sigma$ form a subgroup of the cyclic
group $C_r$. If $r=0$, all such invertible transformations form a
group isomorphic either to a cyclic group $C_n$ or to a dihedral
group $D_n$ depending on whether all such transformations are
orientation preserving or not. Applied to the tangent image of
planar closed curves, this generalizes a result of Bisztriczky and
Rival [1]. The proof rests on the theorem: {\it Let
$\Delta\colon\bbd R\to\bbd R$ be continuous, nowhere constant, and
$\lim_{x\to -\infty}\Delta(x)=-\infty$, $ \lim_{x\to+\infty}\Delta
(x)=+\infty$; then the only continuous map $\Sigma\colon\bbd R\to\bbd
R$ such that $\Delta\circ\Sigma=\Delta$ is the identity
$\Sigma=\id_{\bbd R}$.
Categories:53A04, 55M25, 55M35 |