Search for tag: "3-manifold"

Thumbnail for entry Meeting 13.2: Topological quantum computing and 3-manifold invariants

59:15

Meeting 13.2: Topological quantum computing and…

Meeting 13.2: Topological quantum computing and 3-manifold invariants

Meeting 13.2: Topological quantum computing and 3-manifold invariants

We spell out the precise relation between 3-manifold/knot invariants and the model of topological quantum computing discussed in the previous several meetings.

topological quantum computation
quantum invariants
3-manifold
knots
From  Eric Samperton 27 plays 0  
Date of creation
4/22/2021 12:00 AM
Thumbnail for entry Meeting 2.1: Heegaard splittings of 3-manifolds

58:28

Meeting 2.1: Heegaard splittings of 3-manifolds

Meeting 2.1: Heegaard splittings of 3-manifolds

Meeting 2.1: Heegaard splittings of 3-manifolds

I sketch the proof that every (orientable, closed, PL) 3-manifold has a Heegaard splitting.

3-manifold
heegaard splitting
From  Eric Samperton 29 plays 0  
Date of creation
2/2/2021 12:00 AM
Thumbnail for entry Meeting 1.2: The best dimension is 3

01:05:46

Meeting 1.2: The best dimension is 3

Meeting 1.2: The best dimension is 3

Meeting 1.2: The best dimension is 3

We discuss triangulations of manifolds, and then I justify my hot take that the best dimension is three.

triangulation
piecewise linear manifold
3-dimensional manifold
3-manifold
From  Eric Samperton 55 plays 0  
Date of creation
1/28/2021 12:00 AM