Elliptic spectra, the Witten genus and the theorem of the cube

By M. Ando, M. Hopkins, N. Strickland. 2001

180 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8ca5312a5f76376d68a926e300497a7c7d9e42fe

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. A. Mathew
2. M. Hill
3. Lennart Meier
4. Charles Rezk
5. Tyler Lawson
6. M. Hopkins
7. M. Ando
8. Jacob Lurie

In Mathematical Physics

1. A. Mathew
2. M. Hill
3. Lennart Meier
4. Charles Rezk
5. Tyler Lawson
6. M. Hopkins
7. M. Ando
8. Jacob Lurie

Citations in the corpus

• Representation and character theory in 2-categories (2006, background): “hromatic picture in homotopy theory. In the case n= 2, the theory E 2 is an example of an elliptic cohomology theory. For background on elliptic cohomology, we refer the reader to the introduction of [AHS01]). Just as the representation ring R(G) may be viewed as equivariant K-theory of the one poin”
• The sigma orientation is an H∞ map (2004, background): “In [Hop95, AHS01 ], we introduced the notion of an elliptic spectrum and showed that any elliptic spectrum (E, C, t) admits a canonical MU h 6i orientation”
• Topological modular forms with level structure (2013, methodology): “We being by recalling the following (see [2,6,34]).”
• Algebraic topology and modular forms (2002, background): “ to the rule log(Kφ(z)) = −2 X n>0 gn xn n! . 302 M. J. Hopkins For n>2 the terms gn is independent of the quadratic exponential factor, and is the q-expansion of a modular form of weight n(see [27, 6]). This defines the characteristic map π 0E∞ (MOh8i,tmf) → {(g 2,g 4,···) | g 2n ∈ M 2n ⊗Q}. F”
• Quadratic functions in geometry, topology, and M-theory (2002, methodology): “We will use the result of [36, 6] that a stable exponential characteristic class for SU -bundles is determined by its value on (1 − L1)(1 − L2) which can be any power series h(x, y) ∈ H∗(CP∞ × CP∞) satisfying (1) h(0, 0) = 1; (2) h(x, y) = h(y, x); (3) h(y, z)h(x, y + z) = h(x + y, z)h(x, y).”
• The homology of $\tmf$ (2013, background): “Given an even periodic ring spectrum E, the formal scheme SpfE(CP) is a formal group over E0 (see [1]), and is classified by a morphism q : Spec(E0) → MFG.”
• Affineness and chromatic homotopy theory (2013, background): “This is slightly weaker than the definition in [3], which requires π2E to be the trivial invertible module, that is, to contain a unit.”
• A Survey of Elliptic Cohomology (2009, background): “Our notion of elliptic cohomology theory is essentially the same as the notion of an elliptic spectrum as defined in defined in [4].”
• Topological Modular Forms of Level 3 (2008, background): “ralized elliptic curve over S, and η ∈ Γ(S,ω), an element g ∈ O S, which is compatible with base change and such that g(C,λη) = λ−kg(C,η) for λ ∈ O× S . We write mf k = Γ(M,ω⊗k). An elliptic spectrum [AHS01] is a triple (E,C,φ) consisting of an even periodic ring spectrum E, a generalized elliptic c”