Subject: new Hopf listings
From: Mark Hovey
Date: 02 Oct 2000 13:13:11 -0400
Four new papers this time, all from some energetic guy named Greenlees.
He maintains a bibliography on Hopf as well, under
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Greenlees/greenleesbiblio
Mark Hovey
New papers appearing on hopf between 9/28/00 and 10/2/00.
1.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Greenlees/axiomatic
Title: ``Tate cohomology in axiomatic stable homotopy theory.''
Author: J.P.C.Greenlees
AMS classification numbers: 55U35, 55T99, 55P42, 55P91, 55N91
Address: University of Sheffield, UK
Email: j.greenlees@shef.ac.uk
Abstract: Any smashing localization in an axiomatic stable
homotopy theory in the sense of Hovey-Palmieri-Strickland gives rise to
a Tate theory. Various known versions of Tate cohomology (for example in
commutative algebra, in the cohomology of groups, in equivariant homotopy
theory and in chromatic stable homotopy theory) are considered
from this point of view.
Status: Submitted for publication.
2.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Greenlees/guanajuato
Title: Local cohomology in equivariant topology
Author: J.P.C.Greenlees
AMS classification numbers: 13D45, 19L41, 20Jxx, 55N91, 55N22, 55P43
Address: University of Sheffield, UK
Email: j.greenlees@shef.ac.uk
Abstract: The article (based on talks at the Guanajuato
Workshop on Local Cohomology, December 1999) describes
the role of local homology and
cohomology in understanding the equivariant cohomology and
homology of universal spaces. This brings to light an
interesting duality property related to the Gorenstein
condition. The phenomena are studied and illustrated in
several rather different families of examples. Both
topology and commutative algebra benefit from the connection,
and many interesting questions remain open.
3.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Greenlees/so3q
Title: Rational SO(3)-equivariant cohomology theories
Author: J.P.C.Greenlees
AMS classification numbers: 55N91, 55P42, 55P62, 55P91
Address: University of Sheffield, UK
Email: j.greenlees@shef.ac.uk
Abstract: The results of previous work for the circle and O(2)
are used to give an explicit algebraic
model of the category of rational SO(3)-spectra. This gives a complete
classification of rational SO(3)-equivariant cohomology theories.
A number of new features appear for the first time for this group.
4.
http://hopf.math.purdue.edu/cgi-bin/generate?/pub/Greenlees-Hopkins-Rosu/ellT
Title: Rational S^1-equivariant elliptic cohomology
Authors:J.P.C.Greenlees, M.J.Hopkins and I.Rosu
AMS Class numbers: 55N34, 55N91, 55P42, 55P62
\address{JPCG: Department of Pure Mathematics, Hicks Building,
Sheffield S3 7RH. UK.}
\email{j.greenlees@sheffield.ac.uk}
\address{MJH: Department of Mathematics, MIT, Cambridge, MA 02139-4307, USA.}
\email{mjh@math.mit.edu}
\address{IR: Department of Mathematics, MIT, Cambridge, MA 02139-4307, USA.}
\email{ioanid@math.mit.edu}
Abstract: We give a functorial construction of a rational
$S^1$-equivariant cohomology theory from an elliptic curve equipped
with suitable coordinate data. The
elliptic curve may be recovered from the cohomology theory; indeed,
the value of the cohomology theory on the compactification of an
$S^1$-representation is given by the sheaf cohomology of a suitable
line bundle on the curve. The construction is easy: by considering
functions on the elliptic curve with specified poles one may
write down the representing $S^1$-spectrum
in the first author's algebraic model of rational $S^1$-spectra.
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