There are 8 new papers this time.  

Mark Hovey

New papers appearing on hopf between 6/21/01 and 7/13/01

1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Christensen-Hovey/relative

This is the final version of the paper "Quillen model structures for
relative homological algebra" by J. Daniel Christensen and Mark Hovey.
There are only minor corrections and fairly major spacing changes from
the previous version.  

2.
http://hopf.math.purdue.edu/cgi-bin/generate?/FangF-PanJZ/cl-2-1

Title of Paper :Secondary Brown-Kervaire Quadratic forms and $\pi$-manifolds

Author(s) :Fuquan Fang and Jianzhong Pan

Addresses of Authors:

Fuquan Fang
Nankai Institute of Mathematics, Nankai University,
Tianjin 300071, P.R.C 
email:ffang@sun.nankai.edu.cn

and

Jianzhong Pan
Institute of Math.,Academia Sinica ,Beijing 100080 ,China
email:pjz@math03.math.ac.cn

In this paper we assert that for each $\Phi$-oriented $2n$-manifold (c.f
: Definition 1.1) $M$ where $n\ge 4$ and $n\ne 3(mod 4)$, there is a
well-defined quadratic function $\phi_M: H^{n-1}(M, \Z_4)\to \Q/\Z$, we
call the secondary Brown-Kervaire quadratic forms, so that

\begin{itemize}
\item{ $\phi _{M}(x+y)=\phi _{M}(x)+\phi _{M}(y)+j(x\cup Sq^2y)[M]$},
\item{ the Witt class of $\phi _M$ is a homotopy invariant, if
the Wu class $ v_{n+2-2^i}(\nu _M)=0$ for all $i$.}
\end{itemize}
 where $j: \Z_2 \to \Q/\Z$ is the inclusion homomorphism and
$\nu _M$ the stable normal bundle of $M$.

Among the applications we obtain a complete classification of
$(n-2)$-connected $2n$-dimensional $\pi$-manifolds up to
homeomorphism and homotopy equivalence, where $n\geq 4$ and
$n+2\neq 2^i$ for any $i$. In particular, we prove that the
homotopy type of such manifolds determine their homeomorphism
type.

3.
http://hopf.math.purdue.edu/cgi-bin/generate?/PanJZ/cocat1

Title of Paper :Having the H-space structure is not a generic property
Author(s) : Jianzhong Pan
AMS Classification numbers :55P60,55P45

Addresses of Authors:
Institute of Math.,Academia Sinica ,Beijing 100080 ,China
email:pjz@math03.math.ac.cn

 In this note, we answer in negative a question posed by McGibbon about
the generic property of H-space structure.  In fact we verify the
conjecture of Roitberg. Incidentally, the same example also answers in
negative the open problem 10 in McGibbon.

4.
http://hopf.math.purdue.edu/cgi-bin/generate?/PanJZ/equivar

Title of Paper :Equivariant Phantom maps
Author(s) : Jianzhong Pan
AMS Classification numbers :55P91,55P60
Addresses of Authors:
Institute of Math.,Academia Sinica ,Beijing 100080 ,China
email:pjz@math03.math.ac.cn

 A successful generalization of phantom map theory to the equivariant
case for all compact Lie groups is obtained in this paper.  One of the
key observations is the discovery of the fact that homotopy fiber of
equivariant completion splits as product of equivariant
Eilenberg-Maclane spaces which seems impossible at first sight by the
example of Triantafillou.

5.
http://hopf.math.purdue.edu/cgi-bin/generate?/PanJZ/nonneg

Title of Paper :Rational homotopy theory and nonnegative curvature
Author(s) : Jianzhong Pan
AMS Classification numbers :53C20 53C40 55P10
Addresses of Authors:
Institute of Math.,Academia Sinica ,Beijing 100080 ,China
email:pjz@math03.math.ac.cn

In this note , we answer positively a question by Belegradek and
Kapovitch about the relation between rational homotopy theory and a
problem in Riemannian geometry which asks that total spaces of which
vector bundles over compact nonnegative curved manifolds admit
(complete) metrics with nonnegative curvature.

6.
http://hopf.math.purdue.edu/cgi-bin/generate?/PanJZ-WooMH/genus2-1

Title of Paper :Mislin genus of  maps
Author(s) : Jianzhong Pan and Moo Ha Woo
AMS Classification numbers :55D99
Addresses of Authors:
Jianzhong Pan
Institute of Math.,Academia Sinica ,Beijing 100080 ,China
email:pjz@math03.math.ac.cn

and 

Moo Ha Woo
Department of Mathematics Education , Korea University ,
 Seoul , Korea

In this paper, we prove that the Mislin genus of a (co-)H-map between
(co-)H-spaces under certain natural conditions is a finite abelian group
which generalizes results in Zabrodsky, McGibbon and Hurvitz

7.
http://hopf.math.purdue.edu/cgi-bin/generate?/PanJZ-WooMH/phan-elem

Title of Paper :Phantom elements and its Applications
Author(s) : Jianzhong Pan and Moo Ha Woo
AMS Classification numbers :55P10,55P60,55P62,55R10
Addresses of Authors:
Jianzhong Pan
Institute of Math.,Academia Sinica ,Beijing 100080 ,China
email:pjz@math03.math.ac.cn

and 

Moo Ha Woo
Department of Mathematics Education , Korea University ,
 Seoul , Korea

In our previous work, a relation between Tsukiyama problem about self
homotopy equivalence was found by using a generalization of phantom
map. In this note , fundamental result is established for such a
generalization. This is the first time one can deal with phantom maps to
space not satisfying finite type condition.  Application to Forgetful
map is also discussed briefly.

8.
http://hopf.math.purdue.edu/cgi-bin/generate?/Vavpetic-Viruel/f4at2

On the Homotopy type of the Classifying Space 
of the Exceptional Lie Group of Rank 4 

A. VAVPETIC (ales.vavpetic@fmf.uni-lj.si)
Fakulteta za Matematiko in Fiziko
Univerza v Ljubljani
Jadranska 19
1111 Ljubljana
Slovenija

and

A. VIRUEL (viruel@agt.cie.uma.es)
Departamento de Algebra, Geometria y Topologia
Universidad de Malaga
AP. 59
29080 Malaga
Spain 

AMS Classification numbers: 55R35, 55P15

Previous work of several authors shows that the exceptional 
Lie group of rank 4, F_4, as a p-compact group, is determined 
up to isomorphism by the isomorphism type of its maximal torus 
normalizer for p>2. This paper considers the case p=2 proving
that F_4 as 2-compact group is also determined up to isomorphism 
by the isomorphism type of its maximal torus normalizer. This 
allows the authors to determine the integral homotopy type of 
F_4 among connected finite loop spaces with maximal tori.