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Results tagged with gt.geometric-topology
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user 16959
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).
5
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4
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Is the intersection of boundaries of convex bodies a topological sphere?
Let $K_1, K_2, \ldots K_n$ be convex bodies in $R^d$. Assume that for any index set $I$, $\cap_{i \in I} K_i$ is not empty and is not properly contained in any body $K_i$ for $i\in I$.
Is it true tha …
- 1,303
15
votes
Is there a "knot theory" for graphs?
Yes, there are many such results. Conway-Gordon, Sachs in the 80s proved that any map $K_6 \to R^3$ contains two disjoint linked traingles. Robertson-Seymour-Thomas proved found the family of minors …
- 1,303
18
votes
2
answers
980
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A direct proof of the Harer-Zagier recursion enumerating the ways to paste a 2n-gon to get a...
In a 1986 paper, Harer and Zagier proved the recursion:
$$(n+1)e(g,n)=(4n-2)e(g,n-1)+(2n-1)(n-1)(2n-3)e(g-1,n-2)$$
where e(g,n) is the number of ways of grouping sides $S_1...S_{2n}$ of a 2n-gon int …
- 1,303