We construct stable operations Tn: E``âˆ—( ) âˆ’â†’ E``(1/n)âˆ—( ) for n > 0 in the version of elliptic cohomology where the coefficient ring E``âˆ— agrees with the ring of modular forms for SL2(Z) which areâ€¦ (More)

In this paper we analyse the homotopy type at primes p > 3 of the ring spectrum E`` representing a version of elliptic cohomology whose coefficient ring E``âˆ— agrees with the ring of modular forms forâ€¦ (More)

It is clear that the most fundamental issue for the aircraft designer in the early definition phases of the design process is the effect that requirements have on the system. Requirements driveâ€¦ (More)

This is the first of two interconnected parts: Part I contains the geometric theory of generalized modular forms and their connections with the cooperation algebra for elliptic cohomology, E``âˆ—E``,â€¦ (More)

x0 Introduction. The Morava K-theories K(n) () (for p a prime and 0 < n < 1) form a collection of multiplicative cohomology theories whose central r^ ole in homotopy theory is now well established.â€¦ (More)

The methodology presented in this paper is concerned with the ability to make informed decisions early in the design time line in order to provide a feasible, viable and robust system to theâ€¦ (More)

The methodology presented in this paper is concerned with the ability to make informed decisions early in the design time line in order to provide a feasible, viable and robust system to theâ€¦ (More)

We develop a version of Quillenâ€™s geometric cobordism theory for infinite dimensional separable Hilbert manifolds. This cobordism theory has a graded group structure under the topological unionâ€¦ (More)

Like many natural phenomenon, clouds are often modeled using procedural methods, which may be difficult for an artist to control. In this paper, a freehand sketching system is proposed to control theâ€¦ (More)

Introduction. In our earlier papers [2,3,4,5,6], we investigated stable operations and cooperations in elliptic cohomology and its variants, relating these to known operations on rings of modularâ€¦ (More)