What is...the classification of surfaces?
Goal.
Explaining basic concepts of geometric topology in an intuitive way.
This time.
What is...the classification surfaces? Or: Punctures, handles, projective planes.
Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.
Disclaimer.
Geometric topology is usually the study of manifolds. This can mean manifold things ;-) So to be precise, this video series is mostly about knots, surfaces, three and four manifolds.
Typo.
It should have been "of surfaces", duh...
Slides.
http://www.dtubbenhauer.com/youtube.html
Website with exercises.
http://www.dtubbenhauer.com/lecture-g...
Thumbnail.
https://en.wikipedia.org/wiki/Fundame...
Geometric topology.
https://en.wikipedia.org/wiki/Geometr...
https://en.wikipedia.org/wiki/List_of...
https://en.wikipedia.org/wiki/Manifold
https://en.wikipedia.org/wiki/Knot_(m...)
https://en.wikipedia.org/wiki/Surface...)
https://en.wikipedia.org/wiki/3-manifold
Concepts in geometric topology.
https://en.wikipedia.org/wiki/Knot_in...
https://en.wikipedia.org/wiki/Braid_g...
https://en.wikipedia.org/wiki/Euler_c...
https://en.wikipedia.org/wiki/Mapping...
https://en.wikipedia.org/wiki/Exotic_...
https://en.wikipedia.org/wiki/Poincar...
https://en.wikipedia.org/wiki/Thursto...
https://en.wikipedia.org/wiki/Cobordism
https://en.wikipedia.org/wiki/Unknott...
Applications of geometric topology.
https://physics.stackexchange.com/que...
https://mathoverflow.net/questions/48...
https://math.mit.edu/research/highsch...
Surfaces plus examples.
https://en.wikipedia.org/wiki/Surface...)
https://en.wikipedia.org/wiki/Surface...)
https://en.wikipedia.org/wiki/Manifold
https://en.wikipedia.org/wiki/Sphere
https://en.wikipedia.org/wiki/Torus
https://en.wikipedia.org/wiki/Real_pr...
https://en.wikipedia.org/wiki/Klein_b...
https://en.wikipedia.org/wiki/Categor...
Fundamental polygon.
https://en.wikipedia.org/wiki/Fundame...
https://math.stackexchange.com/questi...
Pictures used.
Pictures from the lecture https://www.dtubbenhauer.com/lecture-...
https://preview.free3d.com/img/2016/1...
https://en.wikipedia.org/wiki/Fundame...
Some books I am using (I sometimes steal some pictures from there).
https://www.math.cuhk.edu.hk/course_b...
https://arxiv.org/abs/1610.02592?cont...
https://www.degruyter.com/document/do...
https://bookstore.ams.org/fourman
https://www.degruyter.com/document/do...
https://bookstore.ams.org/surv-55
https://bookstore.ams.org/gsm-20
KnotAtlas.
http://katlas.math.toronto.edu/wiki/T...
SnapPy.
https://snappy.math.uic.edu/
Mathematica.
http://katlas.org/wiki/The_Mathematic...
https://demonstrations.wolfram.com/Ch...
SageMath.
https://doc.sagemath.org/html/en/refe...
#geometrictopology
#topology
#mathematics