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Lecture
Connected Sum of Torus and RP2
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Related lectures (23)
Surface Classification
Covers the classification of surfaces using polygonal presentations and homeomorphism.
Local Homeomorphisms and Coverings
Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.
Holomorphic Functions: Taylor Series Expansion
Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.
Open Mapping Theorem
Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.
Hamiltonian Homeomorphisms on Surfaces
Explores the action of Hamiltonian homeomorphisms on surfaces and discusses related mathematical concepts.
Building surfaces from equilateral triangles
Explores the construction of Riemann surfaces from equilateral triangles and the dynamics of finite-type maps.
Polygonal Presentations: Classification of Surfaces
Explores the classification of surfaces based on polygonal presentations and the identification of sides and vertices.
Fundamental Groups
Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Bounding the Poisson bracket invariant on surfaces
Covers the concept of bounding the Poisson bracket invariant on surfaces, exploring joint work with A. Logunov and S. Tanny.
Topology of Riemann Surfaces
Covers the topology of Riemann surfaces, focusing on orientation and orientability.
Topology in Computer-Aided Design
Explores how sketches in TopSolid manage seams and cuts of different profile types in Computer-Aided Design.
Surface Classification Applications
Covers the applications of surface classification using mathematical notation and formulas.
Closed Surfaces and Integrals
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Explains closed surfaces like spheres, cubes, and cones without covers, and their traversal and removal of edges.
Geodesics on Surfaces
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Explores geodesics on surfaces, focusing on minimizing distances and properties of paths, with examples like great circles on spheres.
Surface Integrals: Regular Parametrization
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Covers surface integrals with a focus on regular parametrization and the importance of understanding the normal vector.
Surfaces with Variable Curvature
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Explores surfaces with variable curvature, discussing their construction and properties.
Solar Radiation on Mars
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Explains the calculation of solar power reaching Mars and the importance of considering the correct surface area for evaluation.
Curves in Space: Parametric Equations and Surfaces
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Covers the equations for curves and surfaces in space, including parametric and particular surfaces.
Surfaces: Curvature and Development
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Explores surfaces with variable curvature, constant curvature, and gothic surfaces, as well as singularities and the inversion of normals.
The Jordan Curve Theorem
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Explores the Jordan Curve Theorem, illustrating the division of a plane by a simple closed curve into two regions.
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