Course

MATH-225: Topology II - fundamental groups

Lectures in this course (101)

Covers commutative diagrams, homotopy, and constructing topological spaces.

Discusses separation conditions, graph, and saturations in equivalence relations on a space.

Explores the Seifert van Kampen theorem and its applications in calculating fundamental groups.

Delves into homotopy identification, pushout diagrams, colimits, and group fundamental calculations.

Covers separated spaces, saturation properties, and projective spaces, including the real projective plane and compactness.

Covers exercises on attaching 1-cells to intervals in topology.

Covers polygonal performance, homomorphisms, and the Klein bottle in topology.

Covers the definition and examples of topological groups, focusing on actions of groups on spaces.

Covers the construction of a telescope using cylinders on circles and the calculation of fundamental groups for various spaces.

Explores the concept of orbit spaces and group actions in topological spaces, including translations and multiplications.

Covers adjunctions, push outs, colimits, and discrete fibers in coverings, emphasizing group actions and symmetries.

Delves into group actions, coverings, fundamental groups, and homomorphisms in topological spaces.

Explores the properties of the quotient space X/G when X is compact and sometimes separated.

Covers student feedback, group exercises, and fundamental topology concepts, emphasizing the importance of understanding coverings and group actions.

Covers homotopy, quotient spaces, and the universal property in topology.

Explores formogenic spaces, topological groups, quotients, and rotations on the unit sphere.

Explores homomorphisms in topology and delves into Galois theory.

Covers fundamental concepts of topology, group actions, and Galoisian properties.

Explores the identification of the space SO(3) and the topology of SS-space of R₃(R).