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### planar linkage isomorphic to an exotic sphere

I recently came across this paper, which showed that any compact smooth manifold is diffeomorphic to a connected component of the moduli space of a planar linkage. Briefly, if we have an undirected ...
625 views

### Which curves and surfaces are realizable by linkages? references?

Ok, so I try to formulate rigorously the question in the title, for which I am asking for references. My definitions may be flawed, so feel free to adjust/correct them! I care about dimensions 2 and 3 ...
105 views

Given a planar polygonal linkage defined by a sequence of $n$ hinge joints $(j_0,\,\cdots,\,j_{n-1},j_n = j_0)$ with links of fixed lengths $\lbrace\|j_{k+1}-j_k\|=d_k\ |\ 0\le k\lt n\rbrace$ between ...
311 views

### Is there a relationship between the moduli space of spatial polygons and the moduli space of labeled points?

It is well known that the set of all polygons with consecutive side lengths $l_1, \dots, l_n$ in $\mathbb{R}^3$, considered up to rigid motions, is a compact complex manifold. Of course, I am assuming,...
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### A basic question on complete intersection liaisons of curves

I am a beginner in the Linkage theory and would like to clarify certain points I am not sure of. Let $P$ be the Hilbert polynomial of a curve in $\mathbb{P}^3$. Let $L$ be an irreducible component of ...
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### A.J. Galitzer's Ph.D. thesis: On the moduli space of closed polygonal linkages on the 2-sphere

Recently I became curious about moduli spaces of linkages and so I found and began reading some papers of Kapovich and Millson. In the paper Hodge theory and the art of paper folding, the Ph.D. ...
446 views

### Calabi-Yau manifolds and polygonal linkage configuration spaces: related?

I was reading about Calabi-Yau manifolds, about which I know little, and was wondering if these (or related complex manifolds, perhaps K3 surfaces) can be viewed as configuration spaces (or moduli ...