Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1088/1361-6544/adb52d

Web of Science

Language：English   Publishing type：Research paper (scientific journal)   Publisher：Nonlinearity  

In this paper, we provide a natural correspondence of eigenstructures of Jacobian matrices associated with equilibria for appropriately transformed two systems describing finite-time blow-ups for ODEs with quasi-homogeneity in an asymptotic sense. As a corollary, we see that asymptotic expansions of blow-ups proposed in Part I themselves provide a criterion of the existence of blow-ups with an intrinsic gap structure of stability information among two systems. Examples provided in Part I are revisited to show the above correspondence.

DOI： 10.1088/1361-6544/adb52e

Web of Science

Scopus

Language：English   Publishing type：Research paper (scientific journal)   Publisher：International Mathematics Research Notices  

Based on the analogies between mapping class groups and absolute Galois groups, we introduce an arithmetic pro-ℓ analogue of Orr invariants for a Galois element associated with Galois action on étale fundamental groups of punctured projective lines. At the same time, we also introduce pro-ℓ Orr space as an arithmetic analogue of Orr space whose third homotopy group is a target group of Orr invariant. We then determine its rank as ℤℓ-module following Igusa-Orr's computation. Moreover, we investigate its relation with Ellenberg's obstruction to π1-sections associated with lower central series filtration in the context of Grothendieck's section conjecture.

DOI： 10.1093/imrn/rnac138

Scopus

Language：English   Publishing type：Research paper (scientific journal)  

We reconfigure the Milnor invariant of links in terms of central group extensions and unipotent Magnus embeddings. We also develop a diagrammatic computation of the invariant and compute the first non-vanishing invariants of Milnor link and of several other links. Moreover, we refine the original Milnor invariants of higher degree.

DOI： 10.1016/j.topol.2019.106991

Language：English   Publishing type：Research paper (scientific journal)  

Ihara initiated the study of a certain Galois representation that may be seen as an arithmetic analogue of the Artin representation of a pure braid group. We pursue the analogies in Ihara theory further and give foundational results, following some issues and their interrelations in the theory of braids and links such as Milnor invariants, Johnson homomorphisms, Magnus–Gassner cocycles and Alexander invariants, and study relations with arithmetic in Ihara theory.

DOI： 10.4171/PRIMS/53-4-6

Repository Public URL： https://hdl.handle.net/2324/7232606

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