M’s Reviews > Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry > Status Update
M
is on page 16 of 226
Skipped the remaining exercises and read about (abstract and geometric) simplicial complexes. That was pretty straightforward. No idea how to do the Exercise in Subsection 1.5 though.
— Jan 20, 2026 07:05PM
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M
is on page 53 of 226
Read the subsection on the Ham-Sandwich theorem.
For Exercise 1: By the intermediate value theorem, there is a line such that on either half-planes we have half of the mass. Define two new mass distributions by restricting on the half-planes. Apply Ham-Sandwich theorem.
For Exercise 2, consider 4 points in a line L, 3 on another line K such that the "middle" point among the three is the intersection of L and K.
— 10 hours, 45 min ago
For Exercise 1: By the intermediate value theorem, there is a line such that on either half-planes we have half of the mass. Define two new mass distributions by restricting on the half-planes. Apply Ham-Sandwich theorem.
For Exercise 2, consider 4 points in a line L, 3 on another line K such that the "middle" point among the three is the intersection of L and K.
M
is on page 46 of 226
Finished the Chapter on Tucker's lemma. I skipped the algorithmic proof of Tucker's lemma as it seemed long and tedious. The topological proof using the degree of the function is beautiful, quite ingenious. Probably the first time I got how homology could be useful. - 22:48, 09.02.2026.
— Feb 09, 2026 07:49PM
M
is on page 29 of 226
Read till Section 2.2. Most stuff made sense, though I find the exercises not that simple. - 12:40, 29.01.2026
— Jan 29, 2026 09:40AM
M
is on page 17 of 226
Read 1.6 now too, pretty slick! I remember that the moment curve comes up when proving that any graph can be drawn in R^3 using only straight segments. I guess it then makes sense that this strategy works in general.
— Jan 20, 2026 07:39PM
M
is on page 6 of 226
Completed everything till Subsection 1.2. It takes me a bit to really understand it, currently stuck at Exercise 4 of that subsection. But enjoyed it so far, I like it being more to the point and being upfront about nontrivial (not proven) facts that are nonetheless important. I feel like it will help me with Hatcher. - 22:21, 15.01.2026
— Jan 15, 2026 07:21PM
