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.
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: The moduli stack of elliptic curves,
  by André Henriques.
• Chapter 4: The Landweber exact functor theorem.
  by Henning Honhold.
• Chapter 5: Sheaves in homotopy theory.
  by Chris Douglas.
• Chapter 6 [talk by M. J. Hopkins]: A stacky look at complex bordism.
  Draft by Mike Hill.
• Chapter 7: The Hasse square,
  by Tilman Bauer.
• Chapter 8: Universal deformations.
  by Jacob Lurie.
• Chapter 9: Goerss-Hopkins obstruction theory.
  by Vigleik Angeltveit.
• Chapter 10 [talk by M. J. Hopkins]: The string orientation.
  by André Henriques.
• Chapter 11 [talk by M. J. Hopkins]: Towards the construction of tmf
  by André Henriques.
• Chapter 12: The construction of tmf.
  by Mark Behrens.
• Chapter 13: The homotopy groups of tmf and of its localizations.
  by André Henriques.
• Glossary of concepts and terminology.
  by Tilman Bauer, Mark Behrens, Chris Douglas, John Francis, André Henriques, Mike Hill, and Niko Naumann.
• 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.