M. Arkowitz
The semigroup of Self Homotopy Classes Which Induce Zero on
Homotopy Groups
|
|
H. Baues
The number of indecomposable stable homotopy types
with torsion free homology
|
|
P. Booth
On the Classification of Fibrations whose Fibres are
Products of Eilenberg-MacLane Spaces
|
|
Abstract:
The classifying spaces used are function spaces, constructed from the
Eilenberg-MacLane spaces in question. This procedure involves no
simplicial sets, no geometric realizations and no infinite limiting
processes. As a result, computations can be carried out using the
methods of elementary homotopy theory. A group of self homotopy
equivalences, i.e. of the product of the Eilenberg-MacLane spaces,
plays an important role in this argument.
|
|
C. Broto
The monoid of self homotopy equivalences of p-completed classifying spaces of finite groups
|
Abstract:
We study the homnotopy type of the classifying space of the
monoid
of self homotopy equivalences of the p-completed classifying space of a
finite
group G. As an application we compare groups extensions of finite
p-groups by a finite group G with fibrations where the base space
is the classifying space of a finite p-group and fibre
is the p-completion of BG.
(This will be based on joint work with Ran Levi and
Bob Oliver.)
|
|
A. Dold
Spaces of classifying maps
and gauge groups
|
|
D. L. Ferrario
Equivariant index and homotopic classification of self-maps.
|
|
Abstract:
We show some results about
equivariant self homotopy equivalences
of orthogonal spheres, units and idempotents in
the Burnside ring.
|
|
K. Hardie
and
K. Kamps
On the homotopy 2-groupoid of a Hausdorff
space
|
|
Abstract:
In the first part of the talk the definition and theory of the homotopy
2-groupoid of a Hausdorff space will be summarised. In the second
part, as an application, we describe a new homotopy sequence
for Barratt's u-based track groups and a specialisation adapted for
computation of homotopy groups of certain spaces of homotopy
equivalences over B.
|
|
V. Hauschild
Elliptic spaces and Self Homotopy Equivalences
|
|
Abstract:
An elliptic space $X$ is called star-elliptic if $ H^*(X;Q) $ has
no negative derivations. This is equivalent to the fact that
$ \pi_{ev}(aut_0X)\otimes_ZQ $ is zero. It is a conjecture of
S. Halperin that every elliptic space is star-elliptic. It is
shown that for an oriented fibration $ X\to E\to B $ where $ X $
and $ B $ are star-elliptic, then also $ E $ is star-elliptic.
This gives numerous examples of elliptic spaces confirming the
conjecture of Halperin.
|
|
(Click here to see the latex2html conversion)
|
|
|
|
K. Ishiguro
Rational self-equivalences of spaces in the genus of a product of
quaternionic projective spaces.
|
|
Abstract:
The talk will be based on the following paper:
"Rational self-equivalences of spaces in the genus of a product of
quaternionic projective spaces" J. Math. Soc. Japan 51 (1999),no. 1, 45-
-61. by Ishiguro, Kenshi; Moeller, Jesper; Notbohm, Dietrich.
|
|
|
|
D. Kahn
The structure of the Hurewicz homomorphism
|
|
Abstract:
The group of self equivalences acts on homology and homotopy,
but also on the hurewicz homomorphism. this work, joint with chris
schwartz, studies the basic simple cases for the hurewicz map. we show
when it is epi, split epi, mono, split mono or isomorphic in all
dimensions. we supply examples to show that all these basic cases can
occur and are distinct. we also start on similar problems for related
maps, for example we characterize when the hurewicz map is a rational
isomorphism.
|
|
H. Marcum
Join constructions and Hopf invariants
|
|
Abstract:
For each cotriad $A \buildrel{f}\over\leftarrow C
\buildrel{g}\over\rightarrow B$ a Hopf invariant
$\Sigma\Omega{\cal M}(f,g)\to F(i_f)\ast F(i_g)$ is constructed where
${\cal M}(f,g)$ is the double mapping cylinder and where $F(i_{\bullet})$
denotes
the homotopy fiber of the inclusion of base space into mapping cone.
This Hopf invariant is natural on cotriads in an expected way. For the
cotriad $\ast \leftarrow C\rightarrow \ast$ the construction
yields the classical Hopf
invariant $\Sigma\Omega\Sigma C\to \Omega\Sigma C\ast\Omega\Sigma C$
arising from the suspension comultiplication on $\Sigma C$ in the manner
of Berstein-Hilton. For the cotriad $A\leftarrow A\times B
\rightarrow B$ of projection maps a Hopf invariant of the form
$$\Sigma\Omega(A\ast B)\to (A\times\Omega(A\ltimes\Sigma B)\ast
(B\times\Omega(\Sigma A\rtimes B))$$
is obtained where $\ltimes$ and $\rtimes$ denote the half-smash functors.
We establish some properties of this latter example. The
main technical tool is a result giving a sum decomposition of the join
of diagonal maps $\triangle\ast\triangle$.
Recent interest in cotriad Hopf invariants arises in connection with LS
category and cone length of a map.
|
|
(Click here to see the latex2html conversion)
|
|
K. Maruyama
Genus and Self-homotopy equivalence
|
|
Abstract:
It is known that self homotopy equivalences groups are not
genus invariants in general. In this talk, however, we will show that the
subgroup of elements which induce the identity on homotopy groups is a
genus invariant in some cases.
|
|
J. Moller
Homotopy automorphisms of p-compact groups
|
|
Abstract:
In this survey talk I'll try to sketch various aspects of the
theory for loop space automorphisms of p-compact groups.
|
|
K. Morisugi
Hopf constructions, Samelson products and suspension maps
|
|
Abstract:
Let $\alpha\in\pi_p(X)$ and $\beta\in\pi_q(X)$ for an H-
space $(X, \mu)$.
In this paper we will observe the relation between
$\langle E\alpha, E\beta\rangle$ and $E\langle\alpha, \beta\rangle$,
where $E: X \to \Omega\Sigma X$ is the suspension map and
$\langle\quad, \quad\rangle$ is the Samelson product.
Actually, the relation can be described by using the "generalized Hopf
constructions".
As an application, we determine the group $[\Sigma Sp(2), \Sigma Sp(2)]$.
|
|
(Click here to see the latex2html conversion)
|
|
|
|
|
|
|
|
S. Smith
The rational homotopy nilpotency of some spaces of self-equivalences
|
|
Abstract:
We determine the structure of the rational homotopy Lie algebra of the
classifying space Baut1(X) when X is a formal space
with a two-stage
Sullivan minimal model.
Using known cases of a conjecture of S. Halperin,
we compute the center and nilpotency of this graded Lie algebra for a
large class of pure, formal spaces X. The latter invariant gives the
rational homotopical nilpotency of aut1(X); that is,
the length of
the longest rationally essential commutator in this monoid. In certain
special cases, we obtain a rational factorization of
Baut1(X) corresponding to the
algebraic factorization of the rational homotopy
Lie algebra determined by the center.
|
|
M. Spreafico
The classifying space of the gauge group of an SO(3)-bundle over S^2
|
|
Abstract:
Stable homotopy decompositions of the classifying spaces of
the gauge groups of principal SO(3) and U(2)-bundles over the sphere S^2
are obtained using a fibrewise stable splitting theorem for the loop
space of an unreduced suspension. The stable decomposition is related to
a description of the integral cohomology ring.
|
|
G. Triantafillou
On the arithmeticity of the groups of isotopy and
pseudoisotopy classes of diffeomorphisms
|
|
K. Tsukiyama
Equivariant homotopy equivalences and forgetful map
|
|
Abstract:
We consider the forgetful map from the group
of equivariant self equivalences to the group
of non-equivarinat self equivalences. A sufficient
condition to this forgetful map being a monomorphism
is obtained. Several examples are given.
|
|
P. Witbooi
Wedge cancellation and Mislin genus of certain co-H0-spaces
|
|
Abstract:
We obtain some results on non-cancellation of spheres
as wedge summands of certain
co-H0-spaces,
and Mislin genera of such spaces.
The spaces concerned are cones on certain maps X --> Y,
such that one of the spaces is a sphere,
while the other is a wedge of spheres.
We utilize certain results on presentations of
finite Z-modules.
|
|
J.Z. Pan and
M.H. Woo
Phantom maps and forgetful maps
|
|
Abstract:
In this note, we attack a question posed ten years ago by Tsukiyama
about the injectivity of the so called forgetful map. We show that
we can insert the forgetful maps in an exact sequence and that the
problem can be reduced to the computation of the sequence which turns
out unexpectedly to be related to the phantom map problem and the
famous Halperin conjecture in rational homotopy theory.
|
|
K. Xu
On Nilpotent Subgroups of Self Equivalences of Spaces
|
|