Topology: Lecture Notes 2021

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Related lectures (30)

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Topology: Exploring Cohomology and Quotient Spaces

Covers the basics of topology, focusing on cohomology and quotient spaces, emphasizing their definitions and properties through examples and exercises.

Topology: Classification of Surfaces and Fundamental Groups

Discusses the classification of surfaces and their fundamental groups using the Seifert-van Kampen theorem and polygonal presentations.

Topological matter and its exploration

Explores topological matter using quantum gases, covering the SSH and Rice-Mele models, adiabatic pump, and Berry curvature measurement.

Cell Attachment and Homotopy

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

General Manifolds and Topology

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Space Identification: SO(3)

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

Topology: Disk Deprivation

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

Advanced Analysis II: Recap and Open Sets

Covers a recap of Analysis I and delves into the concept of open sets in R^n, emphasizing their importance in mathematical analysis.

Topology: Open Sets, Compactness, and Connectivity

Explores open sets, compactness, and connectivity in topology, covering topological spaces and compact sets.

Homotopy and Quotient Spaces

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