Configuration spaces of points on the circle and hyperbolic Dehn fillings

A purely combinatorial compactification of the configuration space of n (>4) distinct points with equal weights in the real projective line was introduced by M. Yoshida. We geometrize it so that it will be a real hyperbolic cone-manifold of finite volume with dimension n-3. Then, we vary weights for points. The geometrization still makes sense and yields a deformation. The effectivity of deformations arisen in this manner will be locally described in the existing deformation theory of hyperbolic structures when n-3 = 2, 3.Comment: 22 pages, to appear in Topolog

The diagonal slice of Schottky space

An irreducible representation of the free group on two generators X,Y into SL(2,C) is determined up to conjugation by the traces of X,Y and XY. We study the diagonal slice of representations for which X,Y and XY have equal trace. Using the three-fold symmetry and Keen-Series pleating rays we locate those groups which are free and discrete, in which case the resulting hyperbolic manifold is a genus-2 handlebody. We also compute the Bowditch set, consisting of those representations for which no primitive elements in the group generated by X,Y are parabolic or elliptic, and at most finitely many have trace with absolute value at most 2. In contrast to the quasifuchsian punctured torus groups originally studied by Bowditch, computer graphics show that this set is significantly different from the discreteness locus.Comment: 44 pages, 14 figure

Linear slices of the quasifuchsian space of punctured tori

After fixing a marking (V, W) of a quasifuchsian punctured torus group G, the complex length l_V and the complex twist tau_V,W parameters define a holomorphic embedding of the quasifuchsian space QF of punctured tori into C^2. It is called the complex Fenchel-Nielsen coordinates of QF. For a complex number c, let Q_gamma,c be the affine subspace of C^2 defined by the linear equation l_V=c. Then we can consider the linear slice L of QF by QF \cap Q_gamma,c which is a holomorphic slice of QF. For any positive real value c, L always contains the so called Bers-Maskit slice BM_gamma,c. In this paper we show that if c is sufficiently small, then L coincides with BM_gamma,c whereas L has other components besides BM_gamma,c when c is sufficiently large. We also observe the scaling property of L.Comment: 15 pages, 8 figures. arXiv admin note: some text overlap with arXiv:math/020918

ラバーウッド : その供給特性と利用の発展

While the sustainability of timber production in natural forests in Southeast Asia has seemed to be in peril, rubberwood, a by-product of natural rubber production, has attracted more interest and its utilization steadily developed through the 1980's. In the 1990's, however, especially in countries like Malaysia where utilization expanded intensively, a shortage problem has emerged and prices have increased. Since rubberwood production is a secondary concern for farmers, even when there is increased demand the supply doesn't respond to it. This is a problem for rubberwood supply as an industrial resource, differing from other timbers.天然林からの持続的な木材生産が危ぶまれている東南アジアにおいて、天然ゴム(ラテックス)を産出するパラゴムノキの木部ラバーウッドが、1980年代から着実に需要を伸ばしている。資源量が豊富で価格が安いことに加え、あくまでもラテックスを採取した後の廃材を有効に利用しているがゆえに、ラバーウッドは理想的な木材として期待を集め、特に木製家具産業において大量に利用されている。ところが、ラバーウッドは、現時点では価格が低すぎ、生産者は積極的な生産意欲を持たないため、廃材として供給される以上の量が市場に出てこない。つまり、ラバーウッドの供給は、需要の増減に弾力的に反応しないという特性を持つために、需要が拡大したマレーシアでは不足状況が生じ、利用者にとって価格上昇が深刻な問題となりつつある

Finite planar emulators for K_{4,5} - 4K_2 and K_{1,2,2,2} and Fellows' Conjecture

In 1988 Fellows conjectured that if a finite, connected graph admits a finite planar emulator, then it admits a finite planar cover. We construct a finite planar emulator for K_{4,5} - 4K_2. Archdeacon showed that K_{4,5} - 4K_2 does not admit a finite planar cover; thus K_{4,5} - 4K_2 provides a counterexample to Fellows' Conjecture. It is known that Negami's Planar Cover Conjecture is true if and only if K_{1,2,2,2} admits no finite planar cover. We construct a finite planar emulator for K_{1,2,2,2}. The existence of a finite planar cover for K_{1,2,2,2} is still open.Comment: Final version. To appear in European Journal of Combinatoric