Elliptic Cohomology: The motivic Thom isomorphism

@article{Morava2007EllipticCT,
  title={Elliptic Cohomology: The motivic Thom isomorphism},
  author={Jack Morava},
  journal={arXiv: Algebraic Topology},
  year={2007}
}
  • Jack Morava
  • Published 10 June 2003
  • Mathematics
  • arXiv: Algebraic Topology
The existence of a good theory of Thom isomorphisms in some rational category of mixed Tate motives would permit a nice interpolation between ideas of Kontsevich on deformation quantization, and ideas of Connes and Kreimer on a Galois theory of renormalization, mediated by Deligne's ideas on motivic Galois groups. 
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References

SHOWING 1-10 OF 71 REFERENCES
Operads and Motives in Deformation Quantization
The algebraic world of associative algebras has many deep connections with the geometric world of two-dimensional surfaces. Recently, D. Tamarkin discovered that the operad of chains of the little
Cobordism of symplectic manifolds and asymptotic expansions
The cobordism ring of symplectic manifolds defined by V.L. Ginzburg is shown to be isomorphic to the Pontrjagin ring of complex-oriented manifolds with free circle actions. This suggests an
Weil Conjectures, Perverse Sheaves and l'Adic Fourier Transform
I. The General Weil Conjectures (Deligne's Theory of Weights).- II. The Formalism of Derived Categories.- III. Perverse Sheaves.- IV. Lefschetz Theory and the Brylinski-Radon Transform.- V.
Tate Motives and the Vanishing Conjectures for Algebraic K-Theory
We give axioms for a triangulated ℚ-tensor category T, generated by “Tate objects” ℚ(a), which ensure the existence of a canonical weight filtration on T, and additional axioms which give rise to an
Chern classes and the periods of mirrors
We show how Chern classes of a Calabi Yau hypersurface in a toric Fano manifold can be expressed in terms of the holomorphic at a maximal degeneracy point period of its mirror. We also consider the
The Grothendieck theory of dessins d'enfants: The Grothendieck-Teichmüller group and automorphisms of braid groups
We show that the groupsGT` and ĜT defined by Drinfel’d are respectively the automorphism groups of the tower of the “pro-` completions” B n of the Artin braid groups and of their profinite
Galois symmetries of fundamental groupoids and noncommutative geometry
We define motivic iterated integrals on the affine line, and give a simple proof of the formula for the coproduct in the Hopf algebra of they make. We show that it encodes the group law in the
Knots and Feynman Diagrams
1. Introduction 2. Perturbative quantum field theory 3. The Hopf algebra structure of renormalization 4. Rationality: no knots, no transcendentals 5. The simplest link diagrams 6. Necessary topics
Deformations of algebras over operads and Deligne's conjecture
In present paper we develop the deformation theory of operads and algebras over operads. Free resolutions (constructed via Boardman-Vogt approach) are used in order to describe formal moduli spaces
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