Tomasz Elsner

Geometric group theory, Algebraic topology

W semetrze letnim 2008 r. będę prowadził wykład pt. Geometryczna Teoria Grup. Szczegółowe informacje o wykładzie są tutaj.

Pierwsze spotkanie 29 lutego 2008 (piątek) o godz. 10 w sali 602.

Listy zadań: lista 1 - lista 2 - lista 3 - lista 4 - lista 5

Notatki z wykładu cz.I - Notatki z wykładu cz.II - Notatki z wykładu cz.III - Notatki z wykładu cz.IV - Notatki z wykładu cz.V

• Flats and flat torus theorem in systolic spaces

  Abstract: We prove that that minimal surfaces in a systolic complex are almost isometrically embedded and introduce a local condition for such surfaces which implies minimality. We also prove that minimal surfaces are stable under small modification of their boundaries. These results are used to establish the Flat Torus Theorem for systolic complexes.

• Systolic groups with isolated flats

  Abstract: We study possible configurations of flats in an arbitrary systolic complex. We apply the results to prove that a systolic complex has the Isolated Flats Property if and only if it does not contain isometrically embedded triplanes. We also show that systolic groups with the Isolated Flats Property are relatively hyperbolic with respect to their maximal abelian subgroups of rank at least 2 and that they satisfy the Relative Fellow Traveler Property.

• Isometries of systolic spaces

  Abstract: We prove that any isometry of a systolic complex is either elliptic or hyperbolic. This dichotomy has several consequences on groups acting on systolic complexes.

For more references on systolic complexes see here: