WebJan 7, 2024 · structure and ς is a quadratic differential, then there exists a projective structure β such that a - β = q. Moreover, (a - β) + (β - η) = a - η. This all follows from … Webbetween the end points of the rays in the boundary of the moduli space. If, in addition,theendpointscoincide,thentheyareasymptotic. …

TEICHMÜLLER SPACES AND REPRESENTABILITY OFFUNCTORSi1)

Webthe iterated EDM ray space associated to X. This space comes from considering asymptote classes of EDM rays, endowing the set of these with a natural metric, and then … Webonly one set. This signature structure corresponds to a signature in which all multiplicities are equal. In this case, S(r) is the full symmetric group. 2. If s = «, then r = (0, 1, • • -, «), so … phil learney performance

Teichmüller Theory and Applications to Geometry, Topology, and …

WebThe Complex Structure of the Teichmüller Space 479 The symmetric form Re θAθ¯ B(Imz)2 equals s(A,B)= 2 π δA,BLA + A\ / B c log c+1 c−1 −2. (2.7) Here c =cosθp at each intersection point of α ·β or c =coshδ, where δ is the hyperbolic distance from the axis of A to each disjoint axis congruent to the axis of B. (δA,B is the Kronecker symbol equal to 1 if A=B … WebAug 21, 2010 · We prove, however, that the quotient of the augmented Teichmüller space by any finite index subgroup of the Teichmüller modular group has a canonical structure of a complex orbifold. Using this structure, we construct natural maps from {\overline {\mathcal {T}}} to stacks of admissible coverings of stable Riemann surfaces. WebRay structures on Teichmüller Space While there may be many Thurston metric geodesics between a pair of points in Teichm\"uller space, we find that by imposing an additional energy minimization constraint on the geodesics, thought of as limits of harmonic map rays, we select a unique Thurston geodesic through those points. phil learney academy