GENERALIZED GROUP CHARACTERS AND COMPLEX ORIENTED COHOMOLOGY THEORIES
By M. Hopkins, N. Kuhn, D. Ravenel. 2000
218 citations recorded by the source corpus.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/cd76e1bf51773a6852bf5792528ef6e4174e45a8
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- K(N)-local duality for finite groups and groupoids (2000, background): “(This was called L in [14] but we have renamed it to avoid clashes of notation.”
- Nilpotence and descent in equivariant stable homotopy theory (2015, methodology): “For our nilpotence statements, the strategy of our argument, which goes back to ideas of Quillen [63] and is used prominently by Hopkins–Kuhn–Ravenel [36], is that of complex-oriented descent.”
- Generalized orbifold Euler characteristic of symmetric products and equivariant Morava K-theory (2001, unknown): “ over K(d)∗, if it is finite. We are interested in computing Euler characteristic of equivariant d-th Morava K-theory of a G-manifold M: (1-11) χ K(d)∗ G (M) = dimK(d)even(EG×GM)−dimK(d)odd(EG×GM). In [HKR], they calculate this number in terms of M¨obius functions [HKR, Theorem B]. It is a simple obs”
- A Survey of Elliptic Cohomology (2009, methodology): “The significance of these “expected answers” is not yet clear, but they are closely related to the generalized character theory of [16].”
- Generalized moonshine, II: Borcherds products (2009, methodology): “muting elements of the monster to sets of functions on H has been called a generalized character, since it appears to be related to the characters that show up in complex oriented cohomology theories [Hopkins-Kuhn-Ravenel-2000]. We use the notation V\here, even though the monster vertex algebra had ”
- The units of a ring spectrum and a logarithmic cohomology operation (2004, methodology): “In [HKR00], the authors define a character map, which is a ring homomorphism χG: E 0 BG → map(G�, D) GL(�) . Their theorem [ HKR00 , Thm.”
- The sigma orientation is an H∞ map (2004, background): “In Proposition 6.1 we show that the necessary conditions (1.5) and (1.6) are sufficient if we suppose in addition that p is not a zero divisor in E. We have given a direct proof, but our argument amounts to showing that for k ≤ 3, the character map of [ HKR00 ] for E0(DpBU h 2ki +) is injective.”