What are...homology spheres?

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

This time.
What are...homology spheres? Or: Spheres, but not really...

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.

Website with exercises.

Thumbnail.

Geometric topology.

Concepts in geometric topology.

Applications of geometric topology.

The wild world of three manifolds.

Dehn surgery.

Homology spheres.

Pictures used.

Some books I am using (I sometimes steal some pictures from there).

KnotAtlas.

SnapPy.

Mathematica.

SageMath.

#geometrictopology
#topology
#mathematics
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Here comes the best Processor of Topology. Homology and Homotopy group of spheres are extremely important subjects.

Your explanation is clear and lucid. If I am not wrong Homotopy and Homology was first made into work by Poincare.
Love this video.

asiancollegeofteachers
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I was playing around with the fundamental group of the figure 8 knot in GAP and noticed that Hurwitz groups came up as quotients. Then I found a map to the universal central extension of the 2 3 7 triangle group. I think this 7:25 might explain what I stumbled upon. Interesting stuff!

josh