Subject: Hopf listings Dec. 2001
Date: 12 Dec 2001 11:43:37 -0500
From: Mark Hovey
To: dmd1@lehigh.edu
5 new papers this time. There is also a corrected version of the paper
I announced last time on the Lusternik-Schnirelmann category of Sp(3),
by Fernandez-Suarez, Gomez-Tato, Strom, and Tanre.
Mark Hovey
New papers appearing on hopf between 11/13/01 and 12/12/01
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/Dugger-Isaksen/hypercover
Hypercovers in topology
Daniel Dugger, Daniel C. Isaksen
55U35, 14F20, 14F42
Department of Mathematics
Purdue University
West Lafayette, IN 47907
Department of Mathematics
University of Notre Dame
Notre Dame, IN 46556
ddugger@math.purdue.edu
isaksen.1@nd.edu
We show that if U is a hypercover of a topological
space X then the natural map from hocolim U to X is a weak
equivalence. This fact is used to construct topological realization
functors for the A^1-homotopy theory of schemes over real and
complex fields.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/Scannell-Sinha/knotss
A one-dimensional embedding complex
by Kevin P. Scannell and Dev P. Sinha
St. Louis University and Brown University
scannell@slu.edu dps@math.brown.edu
We give the first explicit computations of rational homotopy groups of
spaces of "long knots" in Euclidean spaces. We define a spectral
sequence which converges to these rational homotopy groups whose E^1
term is defined in terms of Lie algebras related to braid groups. For
odd k we establish a vanishing line for this spectral sequence, show the
Euler characteristic of the rows of this E^1 term is zero, and make
calculations of E^2 in a finite range.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/Sinha/localcohom
The geometry of the local cohomology filtration in equivariant bordism
by Dev P. Sinha
Brown University
dps@math.brown.edu
Local cohomology techniques in equivariant homotopy theory, introduced
by John Greenlees, may be applied to understand homology of classifying
spaces through other equivariant data. In this paper we relate the
local cohomology filtration to the families filtration. By doing so, we
may identify geometry codified by the local cohomology filtration in the
setting of equivariant bordism. The constructions which arise are
naturally analyzed by localized K-theory machinery due to Atiyah and
Segal, which we review.
This paper has appeared in Homology, Homotopy and Applications.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/WuJ/coHspacewu
On co-H maps to the suspension of the projective plane
by Jie Wu
Department of Mathematics
National University of Singapore
Singapore 117543
Republic of Singapore
matwuj@nus.edu.sg
We study co-H-maps from a suspension to the suspension of the
projective plane and provide examples of non-suspension 3-cell
co-H-spaces. These (infinitely many) examples are related to the
homotopy groups of the 3-sphere. For each element of
order 2 in $\pi_n(S^3)$, there is a corresponding
non-suspension co-H-space of cells in dimensions 2, 3 and n+2.
Our ideas are to study Hopf invariants in combinatorial way by
using the Cohen groups.
5.
http://hopf.math.purdue.edu/cgi-bin/generate?/WuJ/mod2Moore2-2
Homotopy Theory of the suspensions of the projective plane
by Jie Wu
Department of Mathematics
National University of Singapore
Singapore 117543
Republic of Singapore
matwuj@nus.edu.sg
The homotopy theory of the suspensions of the real projective plane
is largely investigated. The homotopy groups are computed up to
certain range. The decompositions of the self smashes and the loop
spaces are studied with some applications to the Stiefel manifolds.
This paper is essentially from my Ph. D. thesis at Rochester under the
supervise of Fred Cohen, and my joint works with Fred Cohen and
Paul Selick. The group representation theory,
particularly the modular representation theory of symmetric groups,
is used much in this article.
The table of the homotopy groups computed in this article
have been announced without proofs in Cohen's paper in the Handbook of
Algebraic Topology by James.
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