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

@article{Ando2001EllipticST,
title={Elliptic spectra, the Witten genus and the theorem of the cube},
author={Matthew Ando and Michael J. Hopkins and Neil P. Strickland},
journal={Inventiones mathematicae},
year={2001},
volume={146},
pages={595-687}
}
• Published 2001
• Mathematics
• Inventiones mathematicae
The homology of $\mathrm{tmf}$
We compute the mod $2$ homology of the spectrum $\mathrm{tmf}$ of topological modular forms by proving a 2-local equivalence $\mathrm{tmf} \wedge DA(1) \simeq \mathrm{tmf}_1(3) \simeq BP\left \langleExpand Hochschild cohomology and moduli spaces of strongly homotopy associative algebras Motivated by ideas from stable homotopy theory we study the space of strongly homotopy associative multiplications on a two-cell chain complex. In the simplest case this moduli space is isomorphic toExpand Hochschild Cohomology and Moduli Spaces of Strongly Homotopy Associative Algebras Motivated by ideas from stable homotopy theory we study the space of strongly ho-motopy associative multiplications on a two-cell chain complex. In the simplest case this moduli space is isomorphicExpand The universal coefficient theorem and quantum field theory During the 1950s physics was still struggling with the standard model of elementary particles (Glashow, Nucl Phys, 22(4):579, 1961, [1]), renormalization (Wilson, Rev Mod Phys, 47(4):773, 1975, [2])Expand Affineness and chromatic homotopy theory • Mathematics • 2015 Given an algebraic stack$X$, one may compare the derived category of quasi-coherent sheaves on$X$with the category of dg-modules over the dg-ring of functions on$X$. We study the analogousExpand Power operations in orbifold Tate K-theory We formulate the axioms of an orbifold theory with power operations. We define orbifold Tate K-theory, by adjusting Devoto's definition of the equivariant theory, and proceed to construct its powerExpand Elliptic genera of Landau–Ginzburg models over nontrivial spaces • Mathematics, Physics • 2012 In this paper, we discuss elliptic genera of (2,2) and (0,2) supersymmetric Landau-Ginzburg models over nontrivial spaces, i.e., nonlinear sigma models on nontrivial noncompact manifolds withExpand K(1)-local topological modular forms We construct the Witten orientation of the topological modular forms spectrum tmf in the K(1)-local setting by attaching E∞ cells to the bordism theory MO<8>. We also identify the KO-homology of tmfExpand Cubic structures, equivariant Euler characteristics and lattices of modular forms • Mathematics • 2003 We use the theory of cubic structures to give a fixed point Riemann-Roch formula for the equivariant Euler characteristics of coherent sheaves on projective at schemes over$\Z$with a tame actionExpand The sigma orientation is an H-infinity map • Mathematics • 2002 In "Elliptic spectra, the Witten genus, and the Theorem of the cube" (Invent. Math. 146 (2001)), the authors constructed a natural map from the Thom spectrum MU to any elliptic spectrum, called theExpand #### References SHOWING 1-10 OF 78 REFERENCES 3 suppl • 1:3–38, • 1964 Formal schemes and formal groups We set up a framework for using algebraic geometry to study the generalised cohomology rings that occur in algebraic topology. This idea was probably first introduced by Quillen and it underlies muchExpand Weil pairings and Morava K-theory • Mathematics • 2001 Abstract We give a new proof of a special case of a theorem Hopkins and the authors, relating the Morava K-theory of BU〈6〉 to the theory of cubical structures on formal groups. In the process weExpand A Derivation of K theory from M theory • Mathematics, Physics • 2000 We show how some aspects of the K-theory classification of RR fluxes follow from a careful analysis of the phase of the M-theory action. This is a shortened and simplified companion paper to E8Expand Anomalies in string theory with D-branes • Physics, Mathematics • 1999 We analyze global anomalies for elementary Type II strings in the presence of D-branes. Global anomaly cancellation gives a restriction on the D-brane topology. This restriction makes possible theExpand Equivariant elliptic cohomology and rigidity <abstract abstract-type="TeX"><p>Equivariant elliptic cohomology with complex coefficients was defined axiomatically by Ginzburg, Kapranov and Vasserot and constructed by Grojnowski. We give anExpand Formal schemes and formal groups Homotopy-invariant algebraic structures: in honor of • J.M. Boardman, Contemporary Mathematics • 1999 Products on$MU\$-modules
In [2, Chapter V], Elmendorf, Kriz, Mandell and May (hereafter referred to as EKMM) use their new technology of modules over highly structured ring spectra to give new constructions of MU -modulesExpand
Products on M U -modules. Transactions of the
• Products on M U -modules. Transactions of the
• 1999
Elliptic curves and stable homotopy theory I
• preparation
• 1998