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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)

- Igor Kríz
- 1994

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)

- Po Hu, Igor Kríz, Mark Hovey
- 2004

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)

Using the Landweber}Araki theory of Real cobordism and Real-oriented spectra, we de"ne a Real analogue of the Adams}Novikov spectral sequence. This is a new spectral sequence with a potentially calculable E 2 -term. It has versions converging to either the Z/2-equivariant or the non-equivariant stable 2-stems. We also construct a Real analogue of the… (More)

We discuss certain calculations in the 2-complete motivic stable homotopy category over an algebraically closed field of characteristic 0. Specifically, we prove the convergence of motivic analogues of the Adams and AdamsNovikov spectral sequences, and as one application, discuss the 2-complete version of the complex motivic J-homomorphism. MSC: 14F42,… (More)

- Po Hu, Igor Kríz, Edward Witten
- 2004

The main purpose of this paper is to give rigorous mathematical foundations for investigating closed and closed/open conformal field theories (CFT’s) and their anomalies. In physics, the topic of closed/open CFT has been extensively discussed in the literature (see e.g. [8, 19, 20, 7]). Our investigation was originally inspired by two sources: Edward Witten… (More)

- Pavol Hell, David G. Kirkpatrick, Jan Kratochvíl, Igor Kríz
- SIAM J. Discrete Math.
- 1988

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)

- Igor Kríz
- Combinatorica
- 1989

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)

- Igor Kríz
- Graphs and Combinatorics
- 1987