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Let S be the sphere spectrum. We construct an associative, commutative, and unital smash product in a complete and cocomplete categoryMS of “S-modules” whose derived category DS is equivalent to the classical stable homotopy category. This allows a simple and algebraically manageable definition of “S-algebras” and “commutative S-algebras” in terms of(More)
With motivation from algebraic topology, algebraic geometry, and string<lb>theory, we study various topics in differential homological algebra. The work is divided<lb>into five largely independent Parts:<lb>I Definitions and examples of operads and their actions<lb>II Partial algebraic structures and conversion theorems<lb>III Derived categories from a(More)
In this paper, we use conformal field theory to construct a generalized cohomology theory which has some properties of elliptic cohomology theory which was some properties of elliptic cohomology. A part of our presentation is a rigorous definition of conformal field theory following Segal’s axioms, and some examples, such as lattice theories associated with(More)
A two-factor ofG consists ofdisjoint cycles that cover V(G). The authors consider the existence problem for two-factors in which the cycles are restricted to having lengths from a prescribed (possibly infinite) set of integers. Theorems are presented which derive the existence of such restricted two-factors in G from their existence in G u and G v. The(More)
Let g(k) denote the minimum integer m so that for every set S of m integers there is a k-coloring of the set of all integers so that every translate of S meets every color class. It is a well known consequence of the Local Lemma that g(k) is finite for all k. Here we present a new proof for this fact, that yields a very efficient parallel algorithm for(More)
The first known construction of a graph G(n, i) of chromatic number at least n without cycles of length < i was given in [1]. Another, substantially simpler one has been presented in [4]. Both of theese constructions are based on an induction, solving the problem for graphs and hypergraphs simultaneously. From the graph-theoretical point of view, a graph(More)