Subject: new Hopf listings
Date: 07 Oct 2002 08:43:25 +0100
From: nsthov01@newton.cam.ac.uk (M.A. Hovey)
To: dmd1@lehigh.edu
This second part contains 8 new papers, 2 from Moller,
1 from Oliver, and 5, count 'em 5, from YauD.
Mark Hovey
New papers appearing on hopf between 09/11/02 and 10/07/02, part 2
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Moller/ndet
Title of paper: N-determined p-compact groups
Author: Jesper M. Moller
AMS Classification numbers: 55R35, 55P15
Email address of Author: moller@math.ku.dk
Abstract: We consider p-compact groups where p is an odd primes. The
paper contains a classification of p-compact groups, excluding the
E-family, in terms of maximal torus normalizers.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Moller/twocgs
Author: Jesper Moller
Title: The 2-compact groups in the A-family are N-determined
Let G be compact Lie group locally isomorphic to SU(n) for some n. The
2-completion of the classifyong space BG is a 2-compact group in the
A-family. We show that these 2-compact groups are determined up to
isomorphism by their maximal torus normalizers.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Oliver/limz-odd
Author: Bob Oliver
Title: Equivalences of classifying spaces completed at odd primes
We prove here the Martino-Priddy conjecture for an odd prime p: the
p-completions of the classifying spaces of two groups G and G' are
homotopy equivalent if and only if there is an isomorphism between their
Sylow p-subgroups which preserves fusion. A second theorem is a
description for odd p of the group of homotopy classes of self homotopy
equivalences of the p-completion of BG, in terms of automorphisms of a
Sylow p-subgroup of G which preserve fusion in G. These are both
consequences of a technical algebraic result, which says that for an odd
prime p and a finite group G, all higher derived functors of the inverse
limit vanish for a certain functor on the p-subgroup orbit category of G.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/YauD/adic_genus2
Title: On adic genus, Postnikov conjugates, and lambda-rings
Author: Donald Yau
MSC: 55P15; 55N15, 55P60, 55S25
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street
Urbana, IL 61801
dyau@math.uiuc.edu
Sufficient conditions on a space are given which guarantee that the
$K$-theory ring and the ordinary cohomology ring with coefficients over
a principal ideal domain are invariants of, respectively, the adic genus
and the SNT set. An independent proof of Notbohm's theorem on the
classification of the adic genus of $BS^3$ by $KO$-theory
$\lambda$-rings is given. An immediate consequence of these results
about adic genus is that for any positive integer $n$, the power series
ring $\bZ \lbrack \lbrack x_1, \ldots , x_n \rbrack \rbrack$ admits
uncountably many pairwise non-isomorphic $\lambda$-ring structures.
5.
http://hopf.math.purdue.edu/cgi-bin/generate?/YauD/moduli2
Title: Moduli space of filtered lambda-ring structures over a filtered ring
Author: Donald Yau
MSC: 16W70, 13K05, 13F25
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street
Urbana, IL 61801
dyau@math.uiuc.edu
Motivated by recent works on the genus of classifying spaces of compact
Lie groups, here we study the set of filtered $\lambda$-ring structures
over a filtered ring from a purely algebraic point of view. From a
global perspective, we first show that this set has a canonical topology
compatible with the filtration on the given filtered ring. For power
series rings $R \llbrack x \rrbrack$, where $R$ is between $\bZ$ and
$\bQ$, with the $x$-adic filtration, we mimic the construction of the
Lazard ring in formal group theory and show that the set of filtered
$\lambda$-ring structures over $R \llbrack x \rrbrack$ is canonically
isomorphic to the set of ring maps from some ``universal'' ring $U$ to
$R$. From a local perspective, we demonstrate the existence of
uncountably many mutually non-isomorphic filtered $\lambda$-ring
structures over some filtered rings, including rings of dual numbers
over binomial domains, (truncated) polynomial and powers series rings
over torsionfree $\bQ$-algebras.
6.
http://hopf.math.purdue.edu/cgi-bin/generate?/YauD/nonexistence_final_2
Title: Maps to spaces in the genus of infinite quaternionic projective space
Author: Donald Yau
MSC: 55S37, 55S25
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street
Urbana, IL 61801
dyau@math.uiuc.edu
Spaces in the genus of infinite quaternionic projective space which
admit essential maps from infinite complex projective space are
classified. In these cases the sets of homotopy classes of maps are
described explicitly. These results strengthen the classical theorem of
McGibbon and Rector on maximal torus admissibility for spaces in the
genus of infinite quaternionic projective space. An interpretation of
these results in the context of Adams-Wilkerson embedding in integral
$K$-theory is also given.
7.
http://hopf.math.purdue.edu/cgi-bin/generate?/YauD/steenrod_kuhn
Title: Algebra over the Steenrod algebra, lambda-ring, and Kuhn's Realization Conjecture
Author: Donald Yau
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street
Urbana, IL 61801
dyau@math.uiuc.edu
In this paper we study the relationships between operations in
$K$-theory and ordinary mod $p$ cohomology. In particular, conditions
are given under which the mod $p$ associated graded ring of a filtered
$\lambda$-ring is an unstable algebra over the Steenrod algebra. This
result partially extends to the algebraic setting a topological result
of Atiyah about operations on $K$-theory and mod $p$ cohomology for
torsionfree spaces. It is also shown that any polynomial algebra that
is an algebra over the Steenrod algebra can be realized as the mod $p$
associated graded of a filtered $\lambda$-ring. Another observation is
that Atiyah's result gives rise to a $K$-theoretic analogue of Kuhn's
Realization Conjecture concerning the size of spaces in cohomology.
8.
http://hopf.math.purdue.edu/cgi-bin/generate?/YauD/unstable
Title: Unstable $K$-cohomology algebra is filtered lambda-ring
Author: Donald Yau
MSC: 55N20,55N15,55S05,55S25
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street
Urbana, IL 61801
dyau@math.uiuc.edu
Boardman, Johnson, and Wilson gave a precise formulation for an unstable
algebra over a generalized cohomology theory. Modifying their
definition slightly in the case of complex $K$-theory by taking into
account its periodicity, we prove that an unstable algebra for complex
$K$-theory is precisely a filtered $\lambda$-ring, and vice versa.
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