石井 敦 (ISHII, Atsushi)

 
Papers

Preprints:

[33] Atsushi Ishii and Kanako Oshiro,
Twisted derivatives with Alexander pairs for quandles

Publications:

[32] Atsushi Ishii, Masahide Iwakiri, Seiichi Kamada, Jieon Kim, Shosaku Matsuzaki and Kanako Oshiro,
Biquandle (co)homology and handlebody-links,
J. Knot Theory Ramifications 27 (2018), no. 11, 1843011, 33 pp.

[31] Atsushi Ishii, Ryo Nikkuni and Kanako Oshiro,
On calculations of the twisted Alexander ideals for spatial graphs, handlebody-knots and surface-links,
Osaka J. Math. 55 (2018), no. 2, 297--313.

[30] Atsushi Ishii, Masahide Iwakiri, Seiichi Kamada, Jieon Kim, Shosaku Matsuzaki, Kanako Oshiro,
A multiple conjugation biquandle and handlebody-links,
Hiroshima Math. J. 48 (2018), no. 1, 89--117.

[29] Atsushi Ishii,
Handlebody-knots and the development of quandle theory (Japanese),
S\=ugaku 48 (2018), no. 1, 63--80.

[28] Atsushi Ishii and Sam Nelson,
Partially multiplicative biquandles and handlebody-knots,
Contemp. Math. 689 (2017) 159--176.

[27] Scott Carter, Atsushi Ishii, Masahico Saito and Kokoro Tanaka,
Homology for quandles with partial group operations,
Pacific J. Math. 287-1 (2017), 19--48.

[26] Atsushi Ishii,
The Markov theorems for spatial graphs and handlebody-knots with Y-orientations,
Internat. J. Math. 26 (2015), 1550116, 23 pp.

[25] Atsushi Ishii,
A multiple conjugation quandle and handlebody-knots,
Topology Appl. 196 (2015), 492--500.

[24] Atsushi Ishii, Kengo Kishimoto and Makoto Ozawa,
Knotted handle decomposing spheres for handlebody-knots,
J. Math. Soc. Japan 67 (2015), 407--417.

[23] Atsushi Ishii and Akira Masuoka,
Handlebody-knot invariants derived from unimodular Hopf algebras,
J. Knot Theory Ramifications 23 (2014), 1460001, 24 pp.

[22] Atsushi Ishii, Masahide Iwakiri, Yeonhee Jang and Kanako Oshiro,
A $G$-family of quandles and handlebody-knots,
Illinois J. Math. 57 (2013), 817--838.

[21] Kai Ishihara and Atsushi Ishii,
An operator invariant for handlebody-knots,
Fund. Math. 217 (2012), 233--247.

[20] Atsushi Ishii and Masahide Iwakiri,
Quandle cocycle invariants for spatial graphs and knotted handlebodies,
Canad. J. Math. 64 (2012), 102--122.

[19] Atsushi Ishii, Kengo Kishimoto, Hiromasa Moriuchi and Masaaki Suzuki,
A table of genus two handlebody-knots up to six crossings,
J. Knot Theory Ramifications 21 (2012), 1250035, 9 pp.

[18] Atsushi Ishii and Kengo Kishimoto,
A finite type invariant of order at most 4 for genus 2 handlebody-knots is a constant map,
Topology Appl. 159 (2012), 1115--1121.

[17] Atsushi Ishii,
On normalizations of a regular isotopy invariant for spatial graphs,
Internat. J. Math. 22 (2011) 1545--1559.

[16] Atsushi Ishii and Kengo Kishimoto,
The quandle coloring invariant of a reducible handlebody-knot,
Tsukuba J. Math. 35 (2011) 131--141.

[15] Atsushi Ishii and Kengo Kishimoto,
The IH-complex of spatial trivalent graphs,
Tokyo J. Math. 33 (2010) 523--535.

[14] Atsushi Ishii,
The leading finite type coefficients of the Links-Gould polynomial of a link,
Kyungpook Math. J. 50 (2010) 49--58.

[13] Atsushi Ishii, Naoko Kamada and Seiichi Kamada,
The Miyazawa polynomial for long virtual knots,
Topology Appl. 157 (2010) 290--297.

[12] Atsushi Ishii,
Smoothing resolution for the Alexander-Conway polynomial,
Acta Math. Vietnam. 33 (2008) 321--333.

[11] Atsushi Ishii,
Moves and invariants for knotted handlebodies,
Algebr. Geom. Topol. 8 (2008) 1403--1418.

[10] Atsushi Ishii,
The skein index for link invariants,
J. Math. Soc. Japan 60 (2008) 719--740.

[9] Atsushi Ishii, Naoko Kamada and Seiichi Kamada,
The virtual magnetic Kauffman bracket skein module and skein relations for the $f$-polynomial,
J. Knot Theory Ramifications 17 (2008) 675--688.

[8] Atsushi Ishii,
The pole diagram and the Miyazawa polynomial,
Internat. J. Math. 19 (2008) 193--207.

[7] Atsushi Ishii and Taizo Kanenobu,
A relation between the LG polynomial and the Kauffman polynomial,
Topology Appl. 154 (2007) 1407--1416.

[6] Atsushi Ishii,
The Links-Gould polynomial as a generalization of the Alexander-Conway polynomial,
Pacific J. Math. 225 (2006) 273--285.

[5] Atsushi Ishii, David De Wit and Jon Links,
Infinitely many two-variable generalisations of the Alexander-Conway polynomial,
Algebr. Geom. Topol. 5 (2005) 405--418.

[4] Atsushi Ishii and Taizo Kanenobu,
Different links with the same Links-Gould invariant,
Osaka J. Math. 42 (2005) 273--290.

[3] Atsushi Ishii,
Algebraic links and skein relations of the Links-Gould invariant,
Proc. Amer. Math. Soc. 132 (2004) 3741--3749.

[2] Atsushi Ishii,
The Links-Gould invariant of closed 3-braids,
J. Knot Theory Ramifications 13 (2004) 41--56.

[1] Atsushi Ishii,
The Links-Gould invariants of the Kanenobu knots,
Kobe J. Math. 20 (2003) 53--61.

Errata:

[20] p.114 L.11, L.12
H_I^3(R_p;\mathbb{Z}_p)_{R_p} in Osaka, and showed that H_I^3(R_3;\mathbb{Z}_3)_{R_3}
--> H_I^2(R_p;\mathbb{Z}_p)_{R_p} in Osaka, and showed that H_I^2(R_3;\mathbb{Z}_3)_{R_3}

[17] p.1557 Lb.3
_{\Gamma_1^G,\Gamma_2^G}(f)
--> _{\Gamma_1^G,\Gamma_2^G}(f)/2

[17] p.1558 L.12, L.13, L.17 for the proof for G=K_5
(the right-hand side)
--> 2 (the right-hand side)

[11] p.1404 L.3
It was extended to spatial Euler graphs by the author
--> It was extended to spatial Euler graphs by Ishii

[11] p.1416 Proposition 8
$x_{-i}=x_{n-i}$
--> $x_{-i}=x_{p-i}$

[4] p.273 L.12
whose chirality is not undetected by
--> whose chirality is not detected by

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