What is...a handle decomposition?

Goal.
Explaining basic concepts of geometric topology in an intuitive way.

This time.
What is...a handle decomposition? Or: Handles and even more handles!

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.

Slides.
http://www.dtubbenhauer.com/youtube.html

Website with exercises.
http://www.dtubbenhauer.com/lecture-g...

Thumbnail.
https://www.researchgate.net/profile/...

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...

The wild world of four manifolds.
https://en.wikipedia.org/wiki/4-manifold
https://en.wikipedia.org/wiki/Categor...
https://arxiv.org/abs/math/0610700
https://web.stanford.edu/~cm5/4D.pdf
https://bookstore.ams.org/gsm-20
https://global.oup.com/academic/produ...
https://en.wikipedia.org/wiki/Four-di...

Pictures used.
https://en.wikipedia.org/wiki/File:Sp...
https://ars.els-cdn.com/content/image...
https://en.wikipedia.org/wiki/Doughnut
Picture from    • What are...cell complexes?  
https://www.researchgate.net/profile/...

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