HL-homotopy of handlebody-links and Milnor's invariants

Yuka Kotorii; Atsuhiko Mizusawa

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arXiv · 1603.09067

HL-homotopy of handlebody-links and Milnor's invariants

Yuka Kotorii·Atsuhiko Mizusawa

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Abstract

A handlebody-link is a disjoint union of embeddings of handlebodies in $S^3$ and an HL-homotopy is an equivalence relation on handlebody-links generated by self-crossing changes. The second author and Ryo Nikkuni classified the set of HL-homotopy classes of 2-component handlebody-links completely using the linking numbers for handlebody-links. In this paper, we construct a family of invariants for HL-homotopy classes of general handlebody-links, by using Milnor's link-homotopy invariants. Moreover, we give a bijection between the set of HL-homotopy classes of almost trivial handlebody-links and tensor product space modulo some general linear actions, especially for 3- or more component handlebody-links. Through this bijection we construct comparable invariants of HL-homotopy classes.

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BibTeX RIS

Yuka Kotorii, Atsuhiko Mizusawa. 2016-03-30. HL-homotopy of handlebody-links and Milnor's invariants. https://arxiv.org/abs/1603.09067

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