Periodic Cohomology Theories Defined by Elliptic Curves

نویسندگان

  • PETER S. LANDWEBER
  • DOUGLAS C. RAVENEL
  • ROBERT E. STONG
  • R. E. STONG
چکیده

We use bordism theory to construct periodic cohomology theories, which we call elliptic cohomology, for which the cohomology of a point is a ring of modular functions. These are complex-oriented multiplicative cohomology theories, with formal groups associated to the universal elliptic genus studied by a number of authors ([CC, LS, O, W1, Z]). We are unable to find a geometric description for these theories.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Topological modular forms with level structure

The cohomology theory known as Tmf, for “topological modular forms,” is a universal object mapping out to elliptic cohomology theories, and its coefficient ring is closely connected to the classical ring of modular forms. We extend this to a functorial family of objects corresponding to elliptic curves with level structure and modular forms on them. Along the way, we produce a natural way to re...

متن کامل

Rational S 1 - Equivariant Elliptic Cohomology

We give a functorial construction of a rational S 1-equivariant cohomology theory from an elliptic curve equipped with suitable coordinate data. The elliptic curve may be recovered from the cohomology theory; indeed, the value of the cohomology theory on the compactification of an S 1-representation is given by the sheaf cohomology of a suitable line bundle on the curve. The construction is eas...

متن کامل

Elliptic Curves and Algebraic Topology

Elliptic curves enter algebraic topology through “Elliptic cohomology”–really a family of cohomology theories–and their associated “elliptic genera”. • Arithmetic aspect: Modularity of elliptic genera, The spectrum TMF of “topological modular forms” and the calculation of π∗TMF →MF (Z), Hopkins’s proof of Borcherds’ congruences. • Physical aspect: Witten’s approach to elliptic genera via string...

متن کامل

The Elliptic curves in gauge theory, string theory, and cohomology

Elliptic curves play a natural and important role in elliptic cohomology. In earlier work with I. Kriz, these elliptic curves were interpreted physically in two ways: as corresponding to the intersection of M2 and M5 in the context of (the reduction of M-theory to) type IIA and as the elliptic fiber leading to F-theory for type IIB. In this paper we elaborate on the physical setting for various...

متن کامل

Operations in Complex - Oriented Cohomology Theories Related to Subgroups of Formal Groups

Using the character theory of Hopkins-Kuhn-Ravenel and the total power operation in complex cobordism of tom Dieck, we develop a theory of power operations in Landweber-exact cohomology theories. We give a description of the total power operation in terms of the theory of subgoups of formal group laws developed by Lubin. We apply this machinery in two cases. For the cohomology theory Eh, we obt...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004