PHANTOM MAPS AND HOMOLOGY THEORIES (2008)
Abstract. We study phantom maps and homology theories in a stable homotopy
PHANTOM MAPS AND HOMOLOGY THEORIES (2007)
Abstract. We study phantom maps and homology theories in a stable homotopy
Multicurves and equivariant cobordism (2002)
Let A be a finite abelian group. We set up an algebraic framework for studying A-equivariant complex-orientable cohomology theories in terms of a suitable kind of equivariant formal groups. We...
The sigma orientation is an H-infinity map (2002)
Ando, Matthew, Hopkins, Michael J., Strickland, Neil P.
In "Elliptic spectra, the Witten genus, and the Theorem of the cube" (Invent. Math. 146 (2001)), the authors constructed a natural map from the Thom spectrum MU to any elliptic spectrum, called the...
The BP cohomology of elementary abelian groups (2000)
In this paper we study E^*BV_k, where E=BP is a cohomology theory with coefficient ring F_p[v_m,...,v_n] (if m>0) or Z_(p)[v_1,...,v_n] (if m=0). We use ideas from the theory of multiple level...
Formal schemes and formal groups (2000)
We set up a framework for using algebraic geometry to study the generalised cohomology rings that occur in algebraic topology. This idea was probably first introduced by Quillen and it underlies much...
We use the new categories of spectra and MU-modules constructed by Elmendorf, Kriz, Mandell and May to get improved results about multiplicative structures on spectra such as P(n) and E(n),...
The Hopf Rings for KO and KU (2000)
Morton, Dena S. Cowen, Strickland, Neil P.
We compute the mod two homology Hopf rings of the spectra KO and KU. The spaces in these spectra are the infinite classical groups and their coset spaces, and their homology was first calculated in...
We give a new and simpler proof of a result of Hopkins and Gross relating Brown-Comenetz duality to Spanier-Whitehead duality in the K(n)-local stable homotopy category.
K(n)-local duality for finite groups and groupoids (2000)
We define an inner product (suitably interpreted) on the K(n)-local spectrum LG := L_{K(n)}BG_+, where G is a finite group or groupoid. This gives an inner product on E^*BG_+ for suitable K(n)-local...
Chern approximations for generalised group cohomology (1999)
Let G be a finite group, and let E be a generalised cohomology theory, subject to certain technical conditions. We study a certain ring C(E,G) that is the best possible approximation to E^0BG that...
Phantom Maps and Homology Theories (1998)
Christensen, J. Daniel, Strickland, Neil P.
We study phantom maps and homology theories in a stable homotopy category S via a certain Abelian category A. We express the group P(X,Y) of phantom maps X -> Y as an Ext group in A, and give...
Morava E-theory of symmetric groups (1998)
We compute the completed E(n) cohomology of the classifying spaces of the symmetric groups, and relate the answer to the theory of finite subgroups of formal groups.