Knot Theory: The Quadratic Linking Degree

Related lectures (53)

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

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

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

Introduces homology as a tool to distinguish spaces in all dimensions and provides insights into its construction and applications.

Introduces reduced homology groups and explains their properties and applications in topology.

Explores chain homotopy, projective complexes, and homotopy equivalences in chain complexes.

Explains the cup and cap product in algebraic topology and their relation to homology groups.

Covers chain maps, homotopy invariance, homology groups, and induced homomorphisms between cycles and boundaries.

Covers the Hairy Ball Theorem and vector fields on spheres.

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

Explores dimension theory in topological spaces and closed subsets, including height interpretation and additivity.

Covers the definitions and properties of ringed spaces, including morphisms and examples of locally ringed spaces.

Discusses norms, distances, and the classification of open and closed sets in mathematical analysis.

Explores homotopy invariance and its application to homology groups of quotients, showcasing isomorphism and chain homotopy.

Covers the homology of projective space, focusing on cohomology and exact sequences.

Covers the definitions and properties of projective algebraic sets and their applications in algebraic geometry.

Discusses how CW pairs satisfy the homotopy extension property through retractions and homotopy extension properties.

Covers the concepts of interior and closure of a set in a topological space, as well as isolated points and accumulation points.

Explores the concept of category theory, providing examples and discussing the opposite category concept.

Explores the long exact sequence of Ext-modules and their computations in homological algebra.

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