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

  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},
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
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
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
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
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


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
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
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
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