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 handlebodylinks, 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, handlebodyknots and surfacelinks, Osaka J. Math. 55 (2018), no. 2, 297313. [30] Atsushi Ishii, Masahide Iwakiri, Seiichi Kamada, Jieon Kim, Shosaku Matsuzaki, Kanako Oshiro, A multiple conjugation biquandle and handlebodylinks, Hiroshima Math. J. 48 (2018), no. 1, 89117. [29] Atsushi Ishii, Handlebodyknots and the development of quandle theory (Japanese), S\=ugaku 48 (2018), no. 1, 6380. [28] Atsushi Ishii and Sam Nelson, Partially multiplicative biquandles and handlebodyknots, Contemp. Math. 689 (2017) 159176. [27] Scott Carter, Atsushi Ishii, Masahico Saito and Kokoro Tanaka, Homology for quandles with partial group operations, Pacific J. Math. 2871 (2017), 1948. [26] Atsushi Ishii, The Markov theorems for spatial graphs and handlebodyknots with Yorientations, Internat. J. Math. 26 (2015), 1550116, 23 pp. [25] Atsushi Ishii, A multiple conjugation quandle and handlebodyknots, Topology Appl. 196 (2015), 492500. [24] Atsushi Ishii, Kengo Kishimoto and Makoto Ozawa, Knotted handle decomposing spheres for handlebodyknots, J. Math. Soc. Japan 67 (2015), 407417. [23] Atsushi Ishii and Akira Masuoka, Handlebodyknot 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 handlebodyknots, Illinois J. Math. 57 (2013), 817838. [21] Kai Ishihara and Atsushi Ishii, An operator invariant for handlebodyknots, Fund. Math. 217 (2012), 233247. [20] Atsushi Ishii and Masahide Iwakiri, Quandle cocycle invariants for spatial graphs and knotted handlebodies, Canad. J. Math. 64 (2012), 102122. [19] Atsushi Ishii, Kengo Kishimoto, Hiromasa Moriuchi and Masaaki Suzuki, A table of genus two handlebodyknots 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 handlebodyknots is a constant map, Topology Appl. 159 (2012), 11151121. [17] Atsushi Ishii, On normalizations of a regular isotopy invariant for spatial graphs, Internat. J. Math. 22 (2011) 15451559. [16] Atsushi Ishii and Kengo Kishimoto, The quandle coloring invariant of a reducible handlebodyknot, Tsukuba J. Math. 35 (2011) 131141. [15] Atsushi Ishii and Kengo Kishimoto, The IHcomplex of spatial trivalent graphs, Tokyo J. Math. 33 (2010) 523535. [14] Atsushi Ishii, The leading finite type coefficients of the LinksGould polynomial of a link, Kyungpook Math. J. 50 (2010) 4958. [13] Atsushi Ishii, Naoko Kamada and Seiichi Kamada, The Miyazawa polynomial for long virtual knots, Topology Appl. 157 (2010) 290297. [12] Atsushi Ishii, Smoothing resolution for the AlexanderConway polynomial, Acta Math. Vietnam. 33 (2008) 321333. [11] Atsushi Ishii, Moves and invariants for knotted handlebodies, Algebr. Geom. Topol. 8 (2008) 14031418. [10] Atsushi Ishii, The skein index for link invariants, J. Math. Soc. Japan 60 (2008) 719740. [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) 675688. [8] Atsushi Ishii, The pole diagram and the Miyazawa polynomial, Internat. J. Math. 19 (2008) 193207. [7] Atsushi Ishii and Taizo Kanenobu, A relation between the LG polynomial and the Kauffman polynomial, Topology Appl. 154 (2007) 14071416. [6] Atsushi Ishii, The LinksGould polynomial as a generalization of the AlexanderConway polynomial, Pacific J. Math. 225 (2006) 273285. [5] Atsushi Ishii, David De Wit and Jon Links, Infinitely many twovariable generalisations of the AlexanderConway polynomial, Algebr. Geom. Topol. 5 (2005) 405418. [4] Atsushi Ishii and Taizo Kanenobu, Different links with the same LinksGould invariant, Osaka J. Math. 42 (2005) 273290. [3] Atsushi Ishii, Algebraic links and skein relations of the LinksGould invariant, Proc. Amer. Math. Soc. 132 (2004) 37413749. [2] Atsushi Ishii, The LinksGould invariant of closed 3braids, J. Knot Theory Ramifications 13 (2004) 4156. [1] Atsushi Ishii, The LinksGould invariants of the Kanenobu knots, Kobe J. Math. 20 (2003) 5361. Errata:[20] p.114 L.11, L.12H_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 righthand side) > 2 (the righthand 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 $x_{i}=x_{ni}$ > $x_{i}=x_{pi}$ [4] p.273 L.12 whose chirality is not undetected by > whose chirality is not detected by 