Concept

Topological manifold

Related lectures (31)

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Manifolds: Charts and Compatibility

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

Closed Curves and Topological Spaces

Explores closed curves in topological spaces, emphasizing their properties and significance in mathematics.

Forcing of Topological Entropy

Delves into topological entropy in compact manifolds and Reeb flows, emphasizing the forcing of entropy via cylindrical contact homology.

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.

Ruelle resonances for geodesic flow

Explores Ruelle resonances for geodesic flows on non-compact manifolds, emphasizing the role of smoothness and eigenvalues in the dynamics.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Dynamics of Singular Riemann Surface Foliations

Explores the dynamics of singular Riemann surface foliations near singular points and their relation to compact manifolds.

Homotopy Extension Property

Demonstrates how to obtain homotopy equivalences between different spaces using the homotopy extension property.

Flow Equations: Singular SPDEs and Quantum Field Theory

Covers recent research on singular SPDEs and their applications in quantum field theory.

Topology: Homotopy and Projective Spaces

Discusses homotopy, projective spaces, and the universal property of quotient spaces in topology.

Topology: Separation Criteria and Quotient Spaces

Discusses separation criteria and quotient spaces in topology, emphasizing their applications and theoretical foundations.

Topology: Homotopy and Cone Attachments

Discusses homotopy and cone attachments in topology, emphasizing their significance in understanding connected components and fundamental groups.

Dynamics of Steady Euler Flows: New Results

Explores the dynamics of steady Euler flows on Riemannian manifolds, covering ideal fluids, Euler equations, Eulerisable flows, and obstructions to exhibiting plugs.

Retractions, vector fields and tangent bundles: Retractions and vector fields

Introduces retractions and vector fields on manifolds, providing examples and discussing smoothness and extension properties.

Universal Covering

Explores the concept of a universal cover of a topological space and the necessary conditions for a space to have one.

Homology of Riemann Surfaces

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.

Understanding Argadir Pumps

Covers the joint equidistribution of CM points, focusing on the understanding of Argadir pumps.

Lifting Criterion

Explores the lifting criterion for maps between path-connected and locally path-connected spaces.