TOPOLOGICAL COMPLEXITY OF SPATIAL POLYGON SPACES

Let (l) over bar = (l(1),..., l(n)) be an n-tuple of positive real numbers, and let N((l) over bar) denote the space of equivalence classes of oriented n-gons in R-3 with consecutive sides of lengths l(1),...,l(n), identified under translation and rotation of R-3. Using known results about the integral cohomology ring, we prove that its topological complexity satisfies TC(N((l) over bar)) = 2n-5, provided that N((l) over bar) is nonempty and contains no straight-line polygons.