## 41 Citations

On the Adams E 2 -term for elliptic cohomology

- Mathematics
- 2001

We investigate the E2-term of Adams spectral sequence based on elliptic homology. The main results describe this E2-term from a ‘chromatic’ perspective. At a prime p > 3, the Bousfield class of Ell…

Extensions of umbral calculus II: double delta operators, Leibniz extensions and Hattori-Stong theorems

- Mathematics
- 1997

We continue our programme of extending the Roman-Rota umbral calculus to the setting of delta operators over a graded ring E * with a view to applications in algebraic topology and the theory of…

On the geometry of the f-invariant

- Mathematics
- 2008

The f-invariant is a higher version of the e-invariant that takes values in the divided congruences between modular forms; it can be formulated as an elliptic genus of manifolds with corners of…

A ug 2 00 8 On the geometry of the f-invariant

- Mathematics
- 2009

The f -invariant is a higher version of the e-invariant that takes values in the divided congruences between modular forms; it can be formulated as an elliptic genus of manifolds with corners of…

SMOOTH K-THEORY

- Mathematics
- 2009

In this paper we consider smooth extensions of cohomology theo- ries. In particular we construct an analytic multiplicative model of smooth K-theory. We further introduce the notion of a smooth…

ON THE DOUBLE TRANSFER AND THE f-INVARIANT

- MathematicsGlasgow Mathematical Journal
- 2012

Abstract The purpose of this paper is to investigate the algebraic double S1-transfer, in particular the classes in the two-line of the Adams–Novikov spectral sequence which are the image of comodule…

Topological $q$-expansion and the supersymmetric sigma model

- Mathematics
- 2015

The Hamiltonian and Lagrangian formalisms offer two perspectives on quantum field theory. This paper sets up a framework to compare these approaches for the supersymmetric sigma model. The goal is to…

Universal polynomials in lambda rings and the K-theory of the infinite loop space tmf

- Mathematics
- 2006

The algebraic structure of the K-theory of a topological space is described by the more general notion of a lambda ring. We show how computations in a lambda ring are facilitated by the use of Adams…

An effective field theory model for differential elliptic cohomology at the Tate curve

- Mathematics
- 2015

We construct a model for differential elliptic cohomology at the Tate curve whose cocycles are families of 2-dimensional effective supersymmetric field theories. A geometrically-motivated modularity…

On the Adams E 2 E 2 E 2 -term for Elliptic Cohomology

- Mathematics
- 1997

We investigate the E 2-term of Adams spectral sequence based on elliptic homology. The main results describe this E 2-term from a `chromatic' perspective. At a prime p > 3, the Bousseld class of E``…

## References

SHOWING 1-10 OF 60 REFERENCES

Cyclic homology and equivariant homology

- Mathematics
- 1987

The purpose of this paper is to explore the relationship between the cyclic homology and cohomology theories of Connes [9-11], see also Loday and Quillen [20], and "IF equivariant homology and…

A proof of the existence of level 1 elliptic cohomology

- Mathematics
- 1993

Landweber provided two proofs of the existence of (level 2) elliptic cohomology (Lecture Notes in Math., vol. 1326, Springer-Verlag, New York, 1988, pp. 69-93). As Baker pointed out (J. Pure Appl.…

Advanced Topics in the Arithmetic of Elliptic Curves

- Mathematics
- 1994

In The Arithmetic of Elliptic Curves, the author presented the basic theory culminating in two fundamental global results, the Mordell-Weil theorem on the finite generation of the group of rational…

Periodic phenomena in the Adams-Novikov spectral sequence

- Mathematics
- 1977

The problem of understanding the stable homotopy ring has long been one of the touchstones of algebraic topology. Low dimensional computation has proceeded slowly and has given little insight into…

Topological Modular Forms, the Witten Genus, and the Theorem of the Cube

- Mathematics
- 1995

There is a rick mathematical structure attached to the cobordism invariants of manifolds. In the cases described by the index theorem, a generalized cohomology theory is used to express the global…

Elliptic Genera of Level N and Elliptic Cohomology

- Mathematics
- 1994

Elliptic genera of level N have been defined by F. Hirzebruch, generalising the earlier notion of elliptic genus due to S. Ochanine. We show that there are corresponding elliptic cohomology theories…

Manifolds and modular forms

- Mathematics
- 1992

During the winter term 1987/88 I gave a course at the University of Bonn under the title "Manifolds and Modular Forms." Iwanted to develop the theory of "Elliptic Genera" and to leam it myself on…

Elliptic Genera of Level N for Complex Manifolds

- Mathematics
- 1988

My lecture at the Como Conference was a survey on the theory of elliptic genera as developed by Ochanine, Landweber, Stong and Witten. A good global reference are the Proceedings of the 1986…