86 research outputs found
Completions of Z/(p)-Tate cohomology of periodic spectra
We construct splittings of some completions of the Z/(p)-Tate cohomology of
E(n) and some related spectra. In particular, we split (a completion of) tE(n)
as a (completion of) a wedge of E(n-1)'s as a spectrum, where t is shorthand
for the fixed points of the Z/(p)-Tate cohomology spectrum (ie Mahowald's
inverse limit of P_{-k} smash SE(n)). We also give a multiplicative splitting
of tE(n) after a suitable base extension.Comment: 30 pages. Published copy, also available at
http://www.maths.warwick.ac.uk/gt/GTVol2/paper8.abs.htm
Flag manifolds and the Landweber-Novikov algebra
We investigate geometrical interpretations of various structure maps
associated with the Landweber-Novikov algebra S^* and its integral dual S_*. In
particular, we study the coproduct and antipode in S_*, together with the left
and right actions of S^* on S_* which underly the construction of the quantum
(or Drinfeld) double D(S^*). We set our realizations in the context of double
complex cobordism, utilizing certain manifolds of bounded flags which
generalize complex projective space and may be canonically expressed as toric
varieties. We discuss their cell structure by analogy with the classical
Schubert decomposition, and detail the implications for Poincare duality with
respect to double cobordism theory; these lead directly to our main results for
the Landweber-Novikov algebra.Comment: 23 pages. Published copy, also available at
http://www.maths.warwick.ac.uk/gt/GTVol2/paper5.abs.htm
Piecewise Euclidean structures and Eberlein's Rigidity Theorem in the singular case
In this article, we generalize Eberlein's Rigidity Theorem to the singular
case, namely, one of the spaces is only assumed to be a CAT(0) topological
manifold. As a corollary, we get that any compact irreducible but locally
reducible locally symmetric space of noncompact type does not admit a
nonpositively curved (in the Aleksandrov sense) piecewise Euclidean structure.
Any hyperbolic manifold, on the other hand, does admit such a structure.Comment: 28 pages. Published copy, also available at
http://www.maths.warwick.ac.uk/gt/GTVol3/paper13.abs.htm
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