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.
• Chapter 2: Elliptic curves and Modular forms.
  Draft by Carl Mautner.
• Chapter 3: Algebraic stacks.
• Chapter 4: The moduli stack of elliptic curves.
  Draft by André Henriques.
• Chapter 5: The Landweber exact functor theorem.
  Draft by Henning Honhold.
• Chapter 6: E-infinity ring spectra.
• Chapter 7: Sheaves in homotopy theory.
  Draft by Chris Douglas.
• Chapter 8: A stacky look at complex bordism.
  Draft by Mike Hill.
• Chapter 9: The Hasse square.
  Draft by Tilman Bauer.
• Chapter 10: Model categories.
• Chapter 11: Universal deformations.
  Draft by Jacob Lurie.
• Chapter 12: Goerss-Hopkins obstruction theory.
• Chapter 13: The Hopkins-Miller theorem.
• Chapter 14: The string orientation.
  Draft by André Henriques.
• Chapter 15: K(1)-local obstruction theory.
• Chapter 16: The construction of tmf.
  Draft by Mark Behrens.
• Chapter 17: The homotopy groups of tmf.
  Draft by André Henriques.
• Glossary of concepts and terminology.
  Draft
• Picture gallery.
  Adams spectral sequence Ext_A(2)( F₂ , F₂ )  ⇒  π_*(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.