Math 529: Lecture Notes and Videos on Computational Topology
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Copyright: I (Bala Krishnamoorthy) hold the copyright
for all lecture scribes/notes, documents, and other
materials including videos posted on these course web
pages. These materials might not be used for commercial
purposes without my consent.
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Scribes from all lectures
so far (as single big file)
| Lec | Date | Topic(s) | Scribe | Video |
| 1 |
Jan 13 |
syllabus,
connected spaces,
applications: patient
trajectories, interface
features in chemistry, discrete connectivity
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Scb1
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Vid1
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| 2 |
Jan 15 |
topology, open sets, interior, closure, and boundary;
functions, homeomorphism, open disc \(\approx
\mathbb{R}^2\), circle \(\not\approx\) annulus
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Scb2
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Vid2
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| 3 |
Jan 20 |
\(\mathbb{S}^2 \approx \mathbb{R}^2 \cup \{\infty\}\),
stereographic projection, 2-manifold (with boundary),
non/orientable manifolds, 0-, 1-manifolds
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Scb3
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Vid3
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| 4 |
Jan 22 |
finite subcover, compact, Hausdorff, completely separable,
\(d\)-manifold, embedding, \(\mathbb{T}^2, \mathbb{R}P^2,
\mathbb{K}^2\), connected sum
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Scb4
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Vid4
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| 5 |
Jan 27 |
classification of 2-manifolds, \(\mathbb{R}P^2 \, \#
\, \mathbb{R}P^2 \approx \mathbb{K}^2\), simplex,
face, simplicial complex, dimension, underlying space
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Scb5
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Vid5
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| 6 |
Jan 29 |
abstract simplicial complex (ASC), geometric
realization of \(d\)-complex in \(\mathbb{R}^{2d+1}\),
triangulation, ASCs of surfaces
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Scb6
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Vid6
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| 7 |
Feb 3 |
topological invariant, Euler characteristic,
\(\chi(\mathbb{M}_1 \#
\mathbb{M}_2)\)\(=\)\(\chi(\mathbb{M}_1)+\chi(\mathbb{M}_2)-2\),
\(\chi+\)orientability: complete invariant
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Scb7
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Vid7
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Last modified: Tue Feb 03 19:46:18 PST 2026
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