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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeAug 12th 2013
   • (edited Aug 12th 2013)
   • PermaLink
   Author: Urs
   Format: MarkdownItexat _[[Witten genus]]_ I have tried to give a more complete list of pointers to the story of refining the Witten genus to a map of $E_\infty$-ring spectra. Now the references there read as follows: *** The refinement of the Witten genus from values in [[modular forms]] to [[topological modular forms]] and further to a morphism of [[E-∞ rings]], hence to the [[string orientation of tmf]] is due to * [[Michael Hopkins]], _Topological modular forms, the Witten Genus, and the theorem of the cube_, Proceedings of the International Congress of Mathematics, Zürich 1994 ([pdf](http://www.mathunion.org/ICM/ICM1994.1/Main/icm1994.1.0554.0565.ocr.pdf)) * [[Michael Hopkins]], _Algebraic topology and modular forms_, Proceedings of the ICM, Beijing 2002, vol. 1, 283--309 ([arXiv:math/0212397](http://arxiv.org/abs/math/0212397)) * [[Matthew Ando]], [[Michael Hopkins]], [[Charles Rezk]], _Multiplicative orientations of KO-theory and the spectrum of topological modular forms_, 2010 ([pdf](http://www.math.uiuc.edu/~mando/papers/koandtmf.pdf)) {#AndoHopkinsRezk} see also remark 1.4 of * [[Paul Goerss]], _Topological modular forms (after Hopkins, Miller and Lurie)_ ([pdf](http://arxiv.org/PS_cache/arxiv/pdf/0910/0910.5130v1.pdf)). and for more on the [[sigma-orientation]] see * [[Matthew Ando]], _The sigma orientation for analytic circle-equivariant elliptic cohomology_, Geom. Topol. 7 (2003) 91-153 ([arXiv:math/0201092](http://arxiv.org/abs/math/0201092)) *** Similar additions I have made to _[[topological modula form]]_ (which is otherwise an empty entry, alas) and to _[[tmf]]_ itself.

   at Witten genus I have tried to give a more complete list of pointers to the story of refining the Witten genus to a map of $E_\infty$-ring spectra. Now the references there read as follows:

   ---

   The refinement of the Witten genus from values in modular forms to topological modular forms and further to a morphism of E-∞ rings, hence to the string orientation of tmf is due to

   • Michael Hopkins, Topological modular forms, the Witten Genus, and the theorem of the cube, Proceedings of the International Congress of Mathematics, Zürich 1994 (pdf)

   • Michael Hopkins, Algebraic topology and modular forms, Proceedings of the ICM, Beijing 2002, vol. 1, 283–309 (arXiv:math/0212397)

   • Matthew Ando, Michael Hopkins, Charles Rezk, Multiplicative orientations of KO-theory and the spectrum of topological modular forms, 2010 (pdf) {#AndoHopkinsRezk}

   see also remark 1.4 of

   • Paul Goerss, Topological modular forms (after Hopkins, Miller and Lurie) (pdf).

   and for more on the sigma-orientation see

   • Matthew Ando, The sigma orientation for analytic circle-equivariant elliptic cohomology, Geom. Topol. 7 (2003) 91-153 (arXiv:math/0201092)

   ---

   Similar additions I have made to topological modula form (which is otherwise an empty entry, alas) and to tmf itself.