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Results tagged with gt.geometric-topology
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user 156936
Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).
6
votes
1
answer
465
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Abstract simplicial complexes - Reference for an elementary definition of mapping degree for...
I am interested to use the mapping degree for simplicial maps between (oriented) abstract simplicial complexes. What I mean by "elementary": My preference would be to use a definition of mapping degr …
- 10.8k
25
votes
3
answers
1k
views
Algebraic graph invariant $\mu(G)$ which links Four-Color-Theorem with Schrödinger operators...
30 years ago, Yves Colin de Verdière introduced the algebraic graph invariant $\mu(G)$ for any undirected graph $G$, see [1]. It was motivated by the study of the second eigenvalue of certain Schrödin …
- 13.6k
77
votes
4
answers
15k
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What are good mathematical models for spider webs?
Sometimes I see spider webs in very complex surroundings, like in the middle of twigs in a tree or in a bush. I keep thinking “if you understand the spider web, you understand the space around it”. W …
- 111
35
votes
4
answers
4k
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An intelligent ant living on a torus or sphere – Does it have a universal way to find out?
I wanted to ask a question about topological invariants and whether they are connected in a fundamental or universal way. I am not an expert in topology, so please let me ask this question by way of a …
- 1,306
17
votes
1
answer
651
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Graph embeddings in the projective plane: for the 35 forbidden minors, do we know their Coli...
The Graph Minor Theorem of Robertson and Seymour asserts
that any minor-closed graph property is determined by a finite set
of forbidden graph minors. It is a broad generalization e.g. of the Kuratows …
- 9,501
6
votes
2
answers
916
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3-colored triangulations of the sphere $S^2$, and Sperner's Lemma
I noticed something about colored triangulations of the topological sphere $S^2$ and have a question about this.
Observation. If you triangulate the sphere $S^2$ and color the vertices with three co …
- 6,937
74
votes
29
answers
8k
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Proofs where higher dimension or cardinality actually enabled much simpler proof?
I am very interested in proofs that become shorter and simpler by going to higher dimension in $\mathbb R^n$, or higher cardinality. By "higher" I mean that the proof is using higher dimension or card …
- 3,107
18
votes
1
answer
1k
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Sperner's Lemma implies Tucker's Lemma - simple combinatorial proof
Sperner’s Lemma is often called the "combinatorial analog" of Brouwer’s Fixed Point Theorem, and similarly Tucker’s Lemma is often called the combinatorial analog of Borsuk–Ulam’s Theorem.
We can fa …
- 6,937