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A dimensional property of Cartesian product

Michael Levin (2013)

Fundamenta Mathematicae

We show that the Cartesian product of three hereditarily infinite-dimensional compact metric spaces is never hereditarily infinite-dimensional. It is quite surprising that the proof of this fact (and this is the only proof known to the author) essentially relies on algebraic topology.

A Nielsen theory for intersection numbers

Christopher McCord (1997)

Fundamenta Mathematicae

Nielsen theory, originally developed as a homotopy-theoretic approach to fixed point theory, has been translated and extended to various other problems, such as the study of periodic points, coincidence points and roots. In this paper, the techniques of Nielsen theory are applied to the study of intersections of maps. A Nielsen-type number, the Nielsen intersection number NI(f,g), is introduced, and shown to have many of the properties analogous to those of the Nielsen fixed point number. In particular,...

An algebraic model of fibration with the fiber $K (π, n)$ -space.

Berikashvili, N. (1996)

Georgian Mathematical Journal

Formes d'intersection et d'enlacement sur une variété

A. Gramain (1976)

Mémoires de la Société Mathématique de France

h-cobordisms between 1-connected 4-manifolds.

Kreck, Matthias (2001)

Geometry & Topology

Homology theory for real analytic and semianalytic sets

Robert M. Hardt (1975)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Hybrid Reduced and Symmetric Product Spaces.

Michael H. Eggar (1979)

Mathematische Zeitschrift

Intersection homology operations.

R. Mark Goresky (1984)

Commentarii mathematici Helvetici

$L_{2}$ -cohomology and intersection homology of locally symmetric varieties, II

Steven Zucker (1986)

Compositio Mathematica

On the loop homology of complex projective spaces

David Chataur, Jean-François Le Borgne (2011)

Bulletin de la Société Mathématique de France

In this short note we compute the Chas-Sullivan BV-algebra structure on the singular homology of the free loop space of complex projective spaces. We compare this result with computations in Hochschild cohomology.

Rational intersection cohomology of quotient varieties. II.

F. Kirwan (1987)

Inventiones mathematicae

Rational string topology

Yves Félix, Jean-Claude Thomas, Micheline Vigué-Poirrier (2007)

Journal of the European Mathematical Society

We use the computational power of rational homotopy theory to provide an explicit cochain model for the loop product and the string bracket of a simply connected closed manifold $M$ . We prove that the loop homology of $M$ is isomorphic to the Hochschild cohomology of the cochain algebra $C^{*} (M)$ with coefficients in $C^{*} (M)$ . Some explicit computations of the loop product and the string bracket are given.

Whitney-Cartan Product Formulae.

Emery Thomas (1970)

Mathematische Zeitschrift

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Currently displaying 1 – 13 of 13