TOPOLOGICAL MODULAR FORMS [after Hopkins, Miller, and Lurie]

نویسنده

  • Paul G. GOERSS
چکیده

In the early 1970s, Quillen [Qui] noticed a strong connection between 1-parameter formal Lie groups and cohomology theories with a natural theory of Chern classes. The algebraic geometry of these formal Lie groups allowed Morava, Ravenel, and others to make predictions about large scale phenomena in stable homotopy theory, and the resulting theorems completely changed the field. For example, the solution of Ravenel’s nilpotence conjectures by Devinatz, Hopkins, and Smith ([DHS] and [HS]) was one of the great advances of the 1980s.

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

COMPUTATION OF THE HOMOTOPY OF THE SPECTRUM tmf

This paper contains a complete computation of the homotopy ring of the spectrum of topological modular forms constructed by Hopkins and Miller. The computation is done away from 6, and at the (interesting) primes 2 and 3 separately, and in each of the latter two cases, a sequence of algebraic Bockstein spectral sequences is used to compute the E2 term of the elliptic Adams-Novikov spectral sequ...

متن کامل

Η - Invariant and Modular Forms

We show that theAtiyah–Patodi–Singer reducedη-invariant of the twisted Dirac operator on a closed 4m− 1-dimensional spin manifold, with the twisted bundle being the Witten bundle appearing in the theory of elliptic genus, is a meromorphic modular form of weight 2m up to an integral q-series. We prove this result by combining our construction of certain modular characteristic forms associated to...

متن کامل

Multiplicative Orientations of Ko-theory and of the Spectrum of Topological Modular Forms

We describe the space of E∞ spin orientations of KO and the space of E∞ string orientations of tmf.

متن کامل

The Cobordism Hypothesis

Assuming a conjecture about factorization homology with adjoints, we prove the cobordism hypothesis, after Baez–Dolan, Costello, Hopkins–Lurie, and Lurie.

متن کامل

Topological Automorphic Forms on U(1, 1)

The homotopy type and homotopy groups of some spectra TAFGU of topological automorphic forms associated to a unitary similitude group GU of type (1, 1) are explicitly described in quasi-split cases. The spectrum TAFGU is shown to be closely related to the spectrum TMF in these cases, and homotopy groups of some of these spectra are explicitly computed.

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 2009