Topological matter and its exploration

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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.

Topology: Compactness and Continuity

Explores compactness, continuity, and quotient spaces in topology, emphasizing the topology of lines in R² and the properties of compact sets.

Cell Attachment and Homotopy

Covers cell attachment, homotopy, mappings, and universal properties in topology.

Topological matter and its exploration

Explores topological matter using quantum gases, focusing on the SSH problem and edge states.

Space Identification: SO(3)

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

Exploring 4D Topological Phases of Matter

Explores 4D topological phases of matter through quantum simulation and discusses approaches like topological pumping and synthetic dimensions.

Topology: Disk Deprivation

Delves into disk deprivation in topology, showcasing how spaces emerge from this process.

Metric Spaces: Topology and Continuity

Introduces metric spaces, topology, and continuity, emphasizing the importance of open sets and the Hausdorff property.

Homotopy and Quotient Spaces

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

Topological Scattering: From Graphs to Networks

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