Homotopy motions of surfaces in $3$-manifolds

Yuya Koda; Makoto Sakuma

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arXiv · 2011.05766

Homotopy motions of surfaces in $3$-manifolds

Yuya Koda·Makoto Sakuma

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Abstract

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 to a Heegaard splitting.

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Yuya Koda, Makoto Sakuma. 2020-11-11. Homotopy motions of surfaces in $3$-manifolds. https://arxiv.org/abs/2011.05766

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