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An infinitary version of Sperner's Lemma

Aarno Hohti (2006)

Commentationes Mathematicae Universitatis Carolinae

We prove an extension of the well-known combinatorial-topological lemma of E. Sperner to the case of infinite-dimensional cubes. It is obtained as a corollary to an infinitary extension of the Lebesgue Covering Dimension Theorem.

An introduction to the abelian Reidemeister torsion of three-dimensional manifolds

Gwénaël Massuyeau (2011)

Annales mathématiques Blaise Pascal

These notes accompany some lectures given at the autumn school “Tresses in Pau” in October 2009. The abelian Reidemeister torsion for 3 -manifolds, and its refinements by Turaev, are introduced. Some applications, including relations between the Reidemeister torsion and other classical invariants, are surveyed.

Applications of Nielsen theory to dynamics

Boju Jiang (1999)

Banach Center Publications

In this talk, we shall look at the application of Nielsen theory to certain questions concerning the "homotopy minimum" or "homotopy stability" of periodic orbits under deformations of the dynamical system. These applications are mainly to the dynamics of surface homeomorphisms, where the geometry and algebra involved are both accessible.

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