Subject: new Hopf listings
From: Mark Hovey
Date: 14 Sep 2000 11:55:24 -0400
Sorry for the long delay since the last such announcement. One big
factor contributing to the delay is e-mail attachments. Clarence has
trouble dealing with these, and it also messes up my system. So it
would be a big help to us if you could follow the old ftp method, or the
newer web browser method, of uploading papers to Hopf.
14 new papers this time, including the abstract of Larry Smith's paper
that was announced last time.
Mark Hovey
New papers appearing on hopf between 7/16/00 and 9/14/00.
0.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/SmithL/koszulii
(This paper was announced last time without abstract. Here is the abstract.)
Title of Paper: Invariant Theory and the Koszul Complex
Representations of Z/p in Characteristic p
Applications
Author: Larry Smith
AMS Code: 13A50 Invariant Theory
Address: Mathematisches Institut
Bunsenstrasse 3--5
D 37073 Goettingen
Federal republic of germany
e-mail: larry@sunrise.uni-math.gwdg.de
THIS IS a POstScript file.
Summary:
We study the ring of invariants $\F[V]^{\Z/p}$\/, and its derived functors
$H^i(\Z/p\semicolon \F[V])$\/, of the cyclic group $\Z/p$ of prime order
$p$ over
a field $\F$ of characteristic $p$\/. We verify a formula of Ellingsrud and
Skjelbred \cite{norway} for the homological codimension, show
the quotient algebra $\F[V]^{\Z/p}/\Im(\Tr^{\Z/p})$ is Cohen-Macaulay,
and that the ideal
generated by the elements in the image of the transfer homomorphism,
$\Im(\Tr^{\Z/p}) \subset \F[V]^{\Z/p}$\/, is primary of height $n-1$ when $V$
is an $n$-dimensional irreducible representation of $\Z/p$\/.
Using our cohomological computations and a previous result \cite{vectors}
about permutation representations we are able to obtain an upper bound for the
degree of homogeneous forms in a minimal algebra generating set for
$\F[V]^{\Z/p}$\/.
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Ando-Basterra/abwgeec
Title:
The Witten genus and equivariant elliptic cohomology
Authors:
Matthew Ando
mando@math.uiuc.edu
Maria Basterra
basterra@math.uiuc.edu
Department of Mathematics,
The University of Illinois at Urbana-Champaign
Abstract:
We construct a Thom class in complex equivariant elliptic cohomology
extending the equivariant Witten genus. This gives a new proof of the
rigidity of the Witten genus, which exhibits a close relationship to
recent work on non-equivariant orientations of
elliptic spectra.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Ando-Hopkins-Strickland/eswgtc
-2/
Elliptic spectra, the Witten genus, and the theorem of the cube.
(revised version)
M. Ando, M. J. Hopkins, and N. P. Strickland
University of Illinois at Urbana-Champaign
mando@math.uiuc.edu
MIT
mjh@math.mit.edu
University of Sheffield
N.P.Strickland@sheffield.ac.uk
This is a revised version of an earlier paper (1998) with the same title.
We show that every elliptic spectrum receives a natural
MU<6>-orientation. For the elliptic spectrum defined by the Tate
curve, this orientation specializes to the Witten genus. The
naturality of the orientation implies that the modularity of the
Witten genus for MU<6>-manifolds.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Broto-Levi-Oliver/blo1
Homotopy equivalences of p-completed classifying spaces of finite groups
by Carles Broto, Ran Levi, and Bob Oliver
We study homotopy equivalences of p-completions of classifying spaces of
finite groups. To each finite group G and each prime p, we associate a
finite category with the following properties. Two p-completed
classifying spaces BG_p^\wedge and BG'_p^\wedge have the same homotopy
type if and only if the associated categories are equivalent. And the
topological group Aut(BG_p^\wedge) of self equivalences is determined by
the self equivalences of the associated category.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Bruner-Davis-Mahowald/eo2/
Nonimmersions of real projective spaces implied by eo2
Robert R. Bruner
Wayne State University, Detroit, MI 48202
rrb@math.wayne.edu
Donald M. Davis
Lehigh University, Bethlehem, PA 18018
dmd1@lehigh.edu
Mark Mahowald
Northwestern University, Evanston, IL 60201
mark@math.nwu.edu
AMS Classifications: 57R42, 55N20
Abstract: Recently Hopkins and Mahowald constructed a new 2-primary
ring spectrum eo2, satisfying H^*(eo2)=A//A2. We use eo2 to obtain
new results regarding nonimmersions of real projective spaces in
Euclidean space. The method is to say enough about eo2-cohomology
of a product of real projective spaces to obtain nonexistence of
certain axial maps.
5.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Chacholski-Dwyer-Intermont/com
plication
The A-complication of a space
W. Chacholski, W. G. Dwyer, and M. Intermont
Suppose that A is a pointed CW-complex. We look at how difficult
it is to construct an A-cellular space B from copies of A by
repeatedly taking homotopy colimits; this is determined by an ordinal
number called the complication of B. Studying the complication
leads to an iterative technique, based on resolutions, for
constructing the A-cellular approximation CW_A(X) of an arbitrary
space X.
Yale University, New Haven, CT 06520 USA
University of Notre Dame, Notre Dame IN 46556 USA
Kalamazoo College, Kalamazoo MI, 49006 USA
MSC2000: 55P60, 55P99
6.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Fors/AugmHom
Title: Augmental Homology Theory and the Künneth Formula for Topological Joins.
Author: Göran Fors.
AMS Classification numbers: 55N10.
Address: Department of Mathematics, University of Stockholm, SE-106 91
Stockholm, Sweden
E-mail address: goranf@matematik.su.se
We prove topological join versions of the relative Eilenberg-Zilber
Theorem and the relative Künneth Formula. We also express the local
homology groups for topological joins and products in terms the local
homology groups for the factors.
7.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Gorbunov-Malikov-Schechtman/gr
oup-all-fedin1
On chiral differential operators over homogeneous spaces
Vassily Gorbounov, Fyodor Malikov, Vadim Schechtman
V.G.: Department of Mathematics, University of Kentucky,
Lexington, KY 40506, USA;\ vgorb\@ms.uky.edu
F.M.: Department of Mathematics, University of Southern California,
Los Angeles, CA 90089, USA;\ fmalikov\@mathj.usc.edu
V.S.: IHES, 35 Route de Chartres, 91440 Bures-sur-Yvette, France;\
vadik\@ihes.fr
The notion of an algebra of chiral differential operators (cdo for
short) over a smooth algebraic variety X has been studied by the authors
previously.
We give a classification of cdo over X in the following cases:
X=G is an affine algebraic group; X=G/N or G/P where N is a unipotent
subgroup and P is a parabolic subgroup and G is simple (the extension
to the case of a semisimple G being straightforward).
The above sheaves are constructed using the BRST (or quantum
Hamiltonian) reduction of the corresponding cdo's on G. The
classification of cdo over homogeneous spaces is exactly reflected in
the BRST world: namely the square of the corresponding BRST charge is
zero at all levels for G/N, only at the critical level for G/B and is
never zero for G/P.
8.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Ishiguro/G2
"Classifying spaces and a subgroup of the exceptional Lie group G_2"
Kenshi Ishiguro
Mathematics subject classification: 55R35
Abstract: We consider a problem on the conditions of a compact Lie group
that its loop space of the p-completed classifying space be a p-compact
group, as well as some related problems. A previously obtained
necessary condition is shown to be not sufficient. Our counterexample
is given by a quotient group \Gamma_2 of a subgroup of the exceptional
Lie group G_2 at p=3. The 3-adic K-theory of B\Gamma_2 and BG_2 are
isomorphic , though the loop space of the 3-completion of B\Gamma_2 is
not a 3-compact group.
9.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Klein/quinn
Title: The dualizing spectrum of a topological group
Author: John R. Klein
AMS subjclass: Primary: 55P91, 55N91, 55P42, 57P10.
Secondary: 55P25, 20J05,18G15.
Address: Dept. Of Mathematics, Wayne State University, Detroit, MI 48202
e-mail: klein@math.wayne.edu
Abstract: To a topological group G, we assign a
naive G-spectrum D_G, called the "dualizing spectrum" of G.
When the classifying space BG is finitely dominated, we show
that D_G detects Poincare duality in the sense that
BG is a Poincare duality space if and only if D_G is a
homotopy finite spectrum. Secondly, we show that
the dualizing spectrum behaves multiplicatively on certain topological
group extensions. In proving these results we introduce a new tool:
a "norm map" which is defined for any G and for any naive G-spectrum E.
Applications include:
(1) a homotopy theoretic solution to a problem posed by Wall which says that
in a fibration sequence of finitely dominated spaces, the total space
satisfies Poincare duality if and only if the base and fiber do.
(2) An entirely homotopy theoretic construction of the Spivak fibration
of a finitely dominated Poincare duality space.
(3) A new proof of Browder's theorem that every finite H-space satisfies
Poincare duality.
(4) We show how to define a variant of Farrell-Tate cohomology for any
topological or discrete group G, with coefficients
in any naive equivariant cohomology theory E. We prove a vanishing result
for this theory.
In an appendix, we identify the homotopy type of D_G for certain
kinds of groups. The class includes all compact Lie groups, torsion free
arithmetic groups and Bieri-Eckmann duality groups.
(This paper has already been accepted for publication in Math. Annalen.)
10.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Mandell/chains
Cochain Multiplications
Michael A. Mandell
mandell@math.uchicago.edu
Abstract
We describe a refinement of the Eilenberg--Steenrod axioms that provides
a necessary and sufficient condition for functors from spaces to
algebras or E-infty algebras to be naturally quasi-isomorphic to the
singular cochain functor.
11.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/McAuley/revised-hilbert
(This is a revised version of the author's paper proving the
Hilbert-Smith conjecture about certain topological groups being forced
to be Lie. The abstract has appeared at least twice before here, so I
omit it). MH
12.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Pakianathan-YalcinE/nc
Title: On Commuting and Non-Commuting Complexes
Authors: Jonathan Pakianathan and Erg\"un Yal\c c\i n
2000 Mathematics Subject Classification.
Primary: 20J05; Secondary: 06A09, 05E25.
Addresses:
Department of Mathematics
University of Rochester
N.Y., U.S.A.
Department of Mathematics
Bilkent University
Ankara, Turkey
Abstract:
In this paper we study various simplicial complexes associated to the
commutative structure of a finite group $G$. We define $NC(G)$
(resp. $C(G)$) as the complex associated to the poset of pairwise
non-commuting (resp. commuting) sets of nontrivial elements in $G$.
We observe that $NC(G)$ has only one positive dimensional connected
component, which we call $BNC(G)$, and we prove that $BNC(G)$ is simply
connected.
Our main result is a simplicial decomposition formula for $BNC(G)$ which
follows from a result of A. Bj\"orner, M. Wachs and V. Welker on
inflated simplicial complexes. As a corollary we obtain that if $G$ has
a nontrivial center or if $G$ has odd order, then the homology group
$H_{n-1}(BNC(G))$ is nontrivial for every $n$ such that $G$ has a
maximal noncommuting set of order $n$.
We discuss the duality between $NC(G)$ and $C(G)$, and between their
$p$-local versions $NC_p(G)$ and $C_p(G)$. We observe that $C_p(G)$ is
homotopy equivalent to the Quillen complexes $A_p(G)$, and obtain some
interesting results for $NC_p(G)$ using this duality.
Finally, we study the family of groups where the commutative relation is
transitive, and show that in this case, $BNC(G)$ is shellable. As a
consequence we derive some group theoretical formulas for the orders of
maximal non-commuting sets.
13.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/YalcinE/clpg4
Title: Set Covering and Serre's Theorem
on the Cohomology Algebra of a $p$-Group
Author: Erg\" un Yal\c c\i n
2000 Mathematics Subject Classification.
Primary: 20J06; Secondary: 20D15, 20D60, 51E20.
Address:
Department of Mathematics
Bilkent University
Ankara, Turkey
Email: yalcine@math.mcmaster.ca
Abstract:
We define a group theoretical invariant, denoted by $s(G)$, as a
solution of a certain set covering problem, and show that it is closely
related to $chl(G)$, the cohomology length of a $p$-group $G$. By
studying $s(G)$, we improve the known upper bounds for the cohomology
length of a $p$-group, and determine $chl(G)$ completely for
extra-special $2$-groups of real type.
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then
put
You should also transfer an abstract as well. Clarence has explicit
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In particular, your abstract is meant to be read by humans, so should be
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