Topology

Related lectures (31)

Modular curves: Riemann surfaces and transition maps

Covers modular curves as compact Riemann surfaces, explaining their topology, construction of holomorphic charts, and properties.

Homotopy Theory of Chain Complexes

Explores the homotopy theory of chain complexes, focusing on model categories, weak equivalences, and the retraction axiom.

Topology Seminar: Tower Sequences and Homomorphisms

Explores tower sequences, homomorphisms, and their applications in topology, including the computation of homology and the construction of telescopes.

Knot Theory: The Quadratic Linking Degree Log in to Mediaspace to watch this video

Covers the quadratic linking degree in knot theory, exploring its definitions, properties, and significance in algebraic geometry.

Interior Points and Compact Sets Log in to Mediaspace to watch this video

Explores interior points, boundaries, adherence, and compact sets, including definitions and examples.

Simplicial and Singular Homology Equivalence Log in to Mediaspace to watch this video

Demonstrates the equivalence between simplicial and singular homology, proving isomorphisms for finite s-complexes and discussing long exact sequences.

Singular Homology: First Properties Log in to Mediaspace to watch this video

Covers the first properties of singular homology and the preservation of decomposition and path-connected components in topological spaces.

Normed Spaces Log in to Mediaspace to watch this video

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Convergence and Limits in Real Numbers Log in to Mediaspace to watch this video

Explains convergence, limits, bounded sequences, and the Bolzano-Weierstrass theorem in real numbers.

Cellular Homology: Applications Log in to Mediaspace to watch this video

Delves into applying cellular homology to compute homology groups and Euler characteristic, showcasing its practical implications.

Homotopy Extension Property Log in to Mediaspace to watch this video

Introduces the homotopy extension property, exploring conditions for extending continuous maps.