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11
Elliptic spectra, the Witten genus and the theorem of the cube
 Invent. Math
, 1997
"... 2. More detailed results 7 2.1. The algebraic geometry of even periodic ring spectra 7 ..."
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Cited by 96 (18 self)
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2. More detailed results 7 2.1. The algebraic geometry of even periodic ring spectra 7
Power operations in elliptic cohomology and representations of loop groups
 Trans. Amer. Math. Soc
, 2000
"... Abstract. The first part describes power operations in elliptic cohomology in terms of isogenies of the underlying elliptic curve. The second part discusses a relationship between equivariant elliptic cohomology and representations of loop groups. The third part investigates the representation theor ..."
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Cited by 23 (5 self)
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Abstract. The first part describes power operations in elliptic cohomology in terms of isogenies of the underlying elliptic curve. The second part discusses a relationship between equivariant elliptic cohomology and representations of loop groups. The third part investigates the representation theoretic considerations which give rise to the power operations discussed in the first part. Contents
Varieties and local cohomology for chromatic group cohomology rings
 Topology
, 1999
"... where E is a suitable complete periodic complex oriented theory and G is a finite group: we describe its variety in terms of the formal group associated to E, and the category of abelian psubgroups of G. Our results considerably extend those of HopkinsKuhnRavenel [16], and this enables us to obta ..."
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Cited by 19 (11 self)
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where E is a suitable complete periodic complex oriented theory and G is a finite group: we describe its variety in terms of the formal group associated to E, and the category of abelian psubgroups of G. Our results considerably extend those of HopkinsKuhnRavenel [16], and this enables us to obtain information about the associated homology of BG. For example if E is the complete 2periodic version of the JohnsonWilson theory E(n) the irreducible components of the variety of the quotient E (BG)=I k by the invariant prime ideal I k = (p; v 1; : : : ; v k\Gamma1) correspond to conjugacy classes of abelian psubgroups of rank n \Gamma k. Furthermore, if we invert v k the decomposition of the variety into irreducible pieces corresponding to minimal primes becomes a decomposition
Common subbundles and intersections of divisors, preprint
, 2000
"... Abstract. Let V0 and V1 be complex vector bundles over a space X. We use the theory of divisors on formal groups to give obstructions in generalised cohomology that vanish when V0 and V1 can be embedded in a bundle U in such a way that V0 ∩ V1 has dimension at least k everywhere. We study various al ..."
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Abstract. Let V0 and V1 be complex vector bundles over a space X. We use the theory of divisors on formal groups to give obstructions in generalised cohomology that vanish when V0 and V1 can be embedded in a bundle U in such a way that V0 ∩ V1 has dimension at least k everywhere. We study various algebraic universal examples related to this question, and show that they arise from the generalised cohomology of corresponding topological universal examples. This extends and reinterprets earlier work on degeneracy classes in ordinary cohomology or intersection theory. 1.
Real Structures and Morava Ktheories
 KTHEORY
, 2002
"... We show that real kstructures coincide for k = 1, 2 on all formal groups for which multiplication by 2 is an epimorphism. This enables us to give explicit polynomial generators for the Morava K(n)homology of BSpin and BSO for n = 1, 2. ..."
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Cited by 1 (1 self)
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We show that real kstructures coincide for k = 1, 2 on all formal groups for which multiplication by 2 is an epimorphism. This enables us to give explicit polynomial generators for the Morava K(n)homology of BSpin and BSO for n = 1, 2.
REALISING FORMAL GROUPS
, 2002
"... Abstract. We show that a large class of formal groups can be realised functorially by even periodic ring spectra. 1. ..."
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Abstract. We show that a large class of formal groups can be realised functorially by even periodic ring spectra. 1.
CHERN APPROXIMATIONS FOR GENERALISED GROUP COHOMOLOGY
"... Abstract. Let G be a finite group and E is a suitable generalised cohomology theory. We define and study a ring C(E,G) that is the best possible approximation to E 0 BG that can be built using knowledge of the complex representations of G. We give a description of Q⊗C(E,G) in terms of generalised ch ..."
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Abstract. Let G be a finite group and E is a suitable generalised cohomology theory. We define and study a ring C(E,G) that is the best possible approximation to E 0 BG that can be built using knowledge of the complex representations of G. We give a description of Q⊗C(E,G) in terms of generalised characters, and we study some cases in which the map C(E,G) − → E 0 BG is an isomorphism. Let G be a finite group, and let E ∗ be a generalised cohomology theory, subject to certain technical conditions (“admissibility ” in the sense of [5]) recalled in Section 1. Our aim in this paper is to define and study a certain ring C(E,G) that is in a precise sense the best possible approximation to E 0 BG that can be built using only knowledge of the complex representation theory of G. There is a natural map C(E,G) − → E 0 BG, whose image is the subring C(E,G) ≤ E 0 BG generated over E 0 by all Chern classes of all complex representations. There is ample precedent for considering this subring in the parallel case of ordinary cohomology; see for example [15, 16, 4]. However, although the generators of C(E,G) come from representation theory, the same cannot be said for the relations; one purpose of our construction is to remedy this. We also also develop a kind of generalised character theory which gives good information about Q ⊗ C(E,G).