Topological modular forms

This page is the online home of the proceedings of the 2007 Talbot workshop, edited by Chris Douglas, John Francis, André Henriques, and Mike Hill.

As we receive approval from the respective authors, drafts of various chapters and other supplementary material will appear below. Feedback is welcome, and will be especially helpful as we move toward finalizing the content. Comments, suggestions, complaints, requests, etc can be sent to a. g. henriques at uu. nl or to cdouglas, jnkf, or mikehill all at math dot mit dot edu. back to Talbot.

Abstract: tmf is (almost) the global sections of a sheaf of E-infinity ring spectra
on the moduli stack of elliptic curves ... or ... "That was easy!".

• Chapter 1: Historical Overview,
  by Corbett Redden.
• Chapter 2: Elliptic curves and Modular forms.
  by Carl Mautner.
• Chapter 3: Algebraic stacks.
  by Nick Rozenblyum.
• Chapter 4: The moduli stack of elliptic curves,
  by André Henriques.
• Chapter 5: The Landweber exact functor theorem.
  by Henning Honhold.
• Chapter 6: Model categories and structured ring spectra.
  by Andrew Blumberg.
• Chapter 7: Sheaves in homotopy theory.
  by Chris Douglas.
• Chapter 8 [talk by M. J. Hopkins]: A stacky look at complex bordism.
  Draft by Mike Hill.
• Chapter 9: The Hasse square,
  by Tilman Bauer.
• Chapter 10: Universal deformations.
  by Jacob Lurie.
• Chapter 11: Goerss-Hopkins obstruction theory.
  by Vigleik Angeltveit.
• Chapter 12 [talk by M. J. Hopkins]: The string orientation.
  by André Henriques.
• Chapter 13 [talk by M. J. Hopkins]: Towards the construction of tmf
  Draft by John Francis and André Henriques.
• Chapter 14: The construction of tmf.
  by Mark Behrens.
• Chapter 15: The homotopy groups of tmf and of its localizations.
  Draft by André Henriques.
• Glossary of concepts and terminology.
  Draft
• Picture gallery.
  Adams spectral sequence  Ext_A(2)( F₂ , F₂ )  ⇒  π_*(tmf).
  The Adams Novikov spectral sequence for tmf  [by M. J. Hopkins; made in 1993]
  Elliptic spectral sequence   H^q( ℳ_Ell‾; ω^⊗p ) ⇒ π_2p-q(Tmf)

Eventually, we will produce poster-sized prints of these and other pictures of the homotopy groups of tmf, and if we're lucky, include one in the book. If you are interested in the meantime, email cdouglas.