Subject:  new Hopf listings
From: Mark Hovey <hovey@picard.math.wesleyan.edu>
Date: 29 Sep 2000 04:46:48 -0400

Two new papers this time.

Mark Hovey

New papers appearing on hopf between 9/14/00 and 9/28/00.

1.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Lundell/stircenid1

Title: Stirling and Central Factorial Number Identies

Author: Albert T. Lundell

Address: Department of Mathematics, Box 395
                 University of Colorado
                 Boulder, Colorado 80309

E-mail: lundell@euclid.colorado.edu

This paper contains many identities related to Stirling numbers and central
factorial numbers, with an emphasis toward divisibility properties.  The paper
is self-contained and contains proofs of the identities.  There is a short
section relating these numbers to the James numbers U(n,r), i.e., the index of
p_*(\pi_{2n-1}(W_{n,r})\subset\pi_{2n-1}(S^{2n-1}), where p:W_{n,r}\arrow
S^{2n-1} is the fibration of complex Stiefel manifolds.

2.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Menichi/Free_Loop

Title: The cohomology ring of free loop spaces

Author: Luc Menichi

AMS classification numbers:  55P35, 16E40, 55P62, 57T30, 55U10.

address:        Universite d'Angers
                Faculte des Sciences
                Departement de Mathematiques
                2 Boulevard Lavoisier
                49045 ANGERS Cedex 01 - FRANCE
Luc.Menichi@univ-angers.fr

Abstract:
Let $X$ be a simply connected space and $\Bbbk$ a commutative ring.
Goodwillie, Burghelea and Fiedorowiscz proved that the Hochschild
cohomology of the singular chains on the pointed loop space
$HH^{*}S_*(\Omega X)$ is isomorphic to the free loop space
cohomology $H^{*}(X^{S^{1}})$.
We proved that this isomorphism is compatible with both
the cup product on $HH^{*}S_*(\Omega X)$ and on $H^{*}(X^{S^{1}})$.
In particular, we explicit the algebra $H^{*}(X^{S^{1}})$
when $X$ is a suspended space, a complex projective space
or a finite CW-complex of dimension $p$ such
that $\frac {1}{(p-1)!}\in {\Bbbk}$.


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