TY - JOUR
T1 - Homotopy Motions of Surfaces in 3-Manifolds
AU - Koda, Yuya
AU - Sakuma, Makoto
N1 - Funding Information:
Y.K. is supported by Japan Society for the Promotion of Science (JSPS) KAKENHI Grant Numbers JP17H06463 and JP20K03588
Publisher Copyright:
© 2022 The Author(s). Published by Oxford University Press. All rights reserved.
PY - 2023/3/1
Y1 - 2023/3/1
N2 - 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.
AB - 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.
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U2 - 10.1093/qmath/haac017
DO - 10.1093/qmath/haac017
M3 - Article
AN - SCOPUS:85153943896
SN - 0033-5606
VL - 74
SP - 29
EP - 71
JO - Quarterly Journal of Mathematics
JF - Quarterly Journal of Mathematics
IS - 1
ER -