Homotopy Motions of Surfaces in 3-Manifolds

Yuya Koda, Makoto Sakuma

Research output: Contribution to journalArticlepeer-review


We introduce the concept of a homotopy motion of a subset in a manifold and give a systematic study of homotopy motions of surfaces in closed orientable 3-manifolds. This notion arises from various natural problems in 3-manifold theory such as domination of manifold pairs, homotopical behavior of simple loops on a Heegaard surface and monodromies of virtual branched covering surface bundles associated with a Heegaard splitting.

Original languageEnglish
Pages (from-to)29-71
Number of pages43
JournalQuarterly Journal of Mathematics
Issue number1
Publication statusPublished - 2023 Mar 1
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


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