Pushpa Publishing House

Journal Menu

Content

Volume 30 (2024)

Volume 29 (2023)

-->

JP Journal of Geometry and Topology

P and

be pants decompositions of S, and let

be an adjacency-preserving bijection. We prove that if P and

are topologically equivalent, or if

is also adjacency-preserving, then F restricts to bijections between two certain subcollections of curves in P and

- a condition which then implies that either F is induced by a homeomorphism of S, or that

P and

are topologically equivalent, and the graph corresponding to the pants decomposition is isomorphic to the complete graph on four vertices.

The proofs use the well-known correspondence between pants decompositions and connected, 3-regular graphs.

JP Journal of Geometry and Topology
Volume 6, Issue 3, Pages 265 - 287 (November 2006)

RECURSIVE GENERATION AND ADJACENCY IN PANTS DECOMPOSITIONS
William R. Vautaw (USA)

Abstract:
We prove that all possible pants decompositions on compact, connected, orientable surfaces can be obtained via a recursive procedure beginning in the low genus cases.

Second, let S be a closed, connected, oriented surface of genus P and be pants decompositions of S, and let be an adjacency-preserving bijection. We prove that if P and are topologically equivalent, or if is also adjacency-preserving, then F restricts to bijections between two certain subcollections of curves in P and - a condition which then implies that either F is induced by a homeomorphism of S, or that P and are topologically equivalent, and the graph corresponding to the pants decomposition is isomorphic to the complete graph on four vertices.