TY - JOUR
T1 - Arithmetic topology in Ihara theory
T2 - To the memory of professor Akito Nomura
AU - Kodani, Hisatoshi
AU - Morishita, Masanori
AU - Terashima, Yuji
N1 - Funding Information:
H.K. is partly supported by Grants-in-Aid for JSPS Fellows 14J12303. Y.T. is partly supported by Grants-in-Aid for Scientific Research (C) 25400083 and by CREST, JST. We would like to thank Hidekazu Furusho, Masanobu Kaneko, Nariya Kawazumi, Hiroaki Nakamura, Takayuki Oda, Kenji Sakugawa and Takao Satoh for communications. We also thank the referees for comments.
Publisher Copyright:
© 2017 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
KW - Ihara power series
KW - Ihara representation
KW - L-adic Alexander invariants
KW - L-adic Milnor invariants
KW - Pro-l Johnson homomorphisms
KW - Pro-l Magnus-Gassner cocycles
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U2 - 10.4171/PRIMS/53-4-6
DO - 10.4171/PRIMS/53-4-6
M3 - Article
AN - SCOPUS:85032372167
SN - 0034-5318
VL - 53
SP - 629
EP - 688
JO - Publications of the Research Institute for Mathematical Sciences
JF - Publications of the Research Institute for Mathematical Sciences
IS - 4
ER -