TY - JOUR

T1 - DIAGONAL COMPLEXES FOR SURFACES OF FINITE TYPE AND SURFACES WITH INVOLUTION

AU - Panina, G.

AU - Gordon, J.

PY - 2022/1/1

Y1 - 2022/1/1

N2 - Two constructions are studied that are inspired by the ideas of a recent paper by the authors. The diagonal complex D and its barycentric subdivision BD related to an oriented surface of finite type F equipped with a number of labeled marked points. This time, unlike the paper mentioned above, boundary components without marked points are allowed, called holes. The symmetric diagonal complex D inv and its barycentric subdivision BD inv related to a symmetric (=with an involution) oriented surface F equipped with a number of (symmetrically placed) labeled marked points. The symmetric complex is shown to be homotopy equivalent to the complex of a surface obtained by “taking a half” of the initial symmetric surface.

AB - Two constructions are studied that are inspired by the ideas of a recent paper by the authors. The diagonal complex D and its barycentric subdivision BD related to an oriented surface of finite type F equipped with a number of labeled marked points. This time, unlike the paper mentioned above, boundary components without marked points are allowed, called holes. The symmetric diagonal complex D inv and its barycentric subdivision BD inv related to a symmetric (=with an involution) oriented surface F equipped with a number of (symmetrically placed) labeled marked points. The symmetric complex is shown to be homotopy equivalent to the complex of a surface obtained by “taking a half” of the initial symmetric surface.

KW - associahedron

KW - curve complex

KW - Moduli space

KW - ribbon graphs

UR - http://www.scopus.com/inward/record.url?scp=85129977837&partnerID=8YFLogxK

U2 - 10.1090/spmj/1709

DO - 10.1090/spmj/1709

M3 - Article

AN - SCOPUS:85129977837

VL - 33

SP - 165

EP - 484

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 3

ER -