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Results tagged with gt.geometric-topology
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user 20186
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).
11
votes
A convex curve inside the unit circle
This follows easily from the fact that the perimeter of a convex curve is in direct proportion with the mean width, and the width of the curve is in every direction smaller than the width of the circl …
- 5,971
1
vote
Accepted
Parameterizing the space of convex quadrilaterals
Let $R\subseteq P$ be the region $\{(x,y)\in P:x>0,y>0, x+y>1\}$ and let $g:P\to R$ be continuous and bijective. Let $h(p_2, p_3, p_4; (x, y)) = p_3+(p_2-p_3)y + (p_4-p_3)x$. Note that $h: P^4 \to P$ …
- 5,971