Geometric topology assignments typically imply

  • the study of specific topics and theorems of geometric topology, such as handle decompositions, the planar theorem, the dimensional Schönflies theorem, knot theory, local flatness etc.;
  • distinctions between different types of geometric topology (low-dimensional and high-dimensional geometric topology, two-dimensional geometric topology etc.);
  • knowledge of geometric topology manifolds (Whitehead manifolds, Graph manifolds, Orientable manifolds), maps, surfaces (Boy's surface, Roman surface, Steiner surface), spheres etc.

Geometric topology studies manifolds as well as maps between them. Being one of the branches of mathematics, it also involves the applications of other mathematical disciplines. It explains why college and high school students find the course of geometric topology one of the most complicated. They face difficulties coping with their geometric topology assignments, which is always stressful.

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