Homotopy Classes

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Related lectures (31)

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Symmetries and Groups in Quantum Mechanics

Covers the role of symmetries and groups in quantum mechanics, focusing on SU2 and SU3, their properties, and implications for physical theories.

Homotopy Equivalence in Chain Complexes

Explores homotopy equivalence in chain complexes, emphasizing path object construction and left/right homotopy characterization.

Homotopy Theory of Chain Complexes

Explores the homotopy theory of chain complexes, including path object construction and fibrations.

Local structure of totally disconnected locally compact groups II

Explores the local structure of totally disconnected locally compact groups, covering commensurated subgroups, completions, local automorphisms, and the quasi-centre.

Quotient Spaces: Three Ways

Explores three ways to form quotient spaces using group actions and equivalence relations.

Topological Scattering: From Graphs to Networks

Covers defining topological phases for photonic systems using unitary scattering matrices, transitioning from graphs to networks.

Cylinder Construction on Chain Complex

Explores the cylinder construction on a chain complex and its equivalence to chain homotopy.

The Whitehead Lemma: Homotopy Equivalence in Model Categories

Explores the Whitehead Lemma, showing when a morphism is a weak equivalence.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

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.