Zobrazeno 1 - 10
of 29
pro vyhledávání: '"Takefumi Nosaka"'
Publikováno v:
Journal of Algebra. 552:52-67
We define a map from second quandle homology to the Schur multiplier and examine its properties. Furthermore, we express the second homology of Alexander quandles in terms of exterior algebras. Additionally, we present a self-contained proof of its s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c4f24d5ca350163be5b39d5f80361308
https://doi.org/10.1016/j.jalgebra.2019.12.027
https://doi.org/10.1016/j.jalgebra.2019.12.027
Autor:
Takefumi Nosaka
Publikováno v:
Publications of the Research Institute for Mathematical Sciences. 56:173-193
As nilpotent studies in knot theory, we focus on invariants of Milnor, Orr, and Kontsevich. We show that the Orr invariant of degree $ k $ is equivalent to the tree reduction of the Kontsevich invariant of degree $< 2k $. Furthermore, we will see a c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c8c5943bb2dd9bf3f9863828436421d6
https://doi.org/10.4171/prims/56-1-7
https://doi.org/10.4171/prims/56-1-7
Autor:
Takefumi Nosaka
Publikováno v:
Geometriae Dedicata. 204:1-24
We discuss the fundamental (relative) 3-classes of knots (or hyperbolic links), and provide diagrammatic descriptions of the push-forwards with respect to every link-group representation. The point is an observation of a bridge between the relative g
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::451150cd8f558f11f4f9ca2c36f6baa3
https://doi.org/10.1007/s10711-019-00442-4
https://doi.org/10.1007/s10711-019-00442-4
Autor:
Takefumi Nosaka
Publikováno v:
Hiroshima Math. J. 50, no. 2 (2020), 207-222
Given a representation of a link group, we introduce a trilinear form, as a topological invariant. We show that, if the link is either hyperbolic or a knot with malnormality, then the trilinear form equals the pairing of the (twisted) triple cup prod
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0d4658ddf3bed48f27fb3b4e4d19d922
https://projecteuclid.org/euclid.hmj/1595901628
https://projecteuclid.org/euclid.hmj/1595901628
Autor:
Takefumi Nosaka
Given a homomorphism from a link group to a group, we introduce a $K_1$-class in another way, which is a generalization of the 1-variable Alexander polynomial. We compare the $K_1$-class with $K_1$-classes in \cite{Nos} and with Reidemeister torsions
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::032722c97e7cd662a1138b13be2e5fd4
http://arxiv.org/abs/2004.03255
http://arxiv.org/abs/2004.03255
Autor:
Takefumi Nosaka
Publikováno v:
Kodai Math. J. 42, no. 1 (2019), 111-129
We show a de Rham theory for cubical manifolds, and study rational homotopy type of the classifying spaces of smooth quandles. We also show that secondary characteristic classes in \cite{Dup2,DK} produce cocycles of quandles.
15 pages, 1 figure
15 pages, 1 figure
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::063a289685cb0359e07ae93a03c9539c
https://doi.org/10.2996/kmj/1552982509
https://doi.org/10.2996/kmj/1552982509
Autor:
Hisatoshi Kodani, Takefumi Nosaka
Publikováno v:
Topology and its Applications
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 the Milnor link and of se
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3c13b02a09f5739a0c51be7ee6cb1f1a
https://doi.org/10.1016/j.topol.2019.106991
https://doi.org/10.1016/j.topol.2019.106991
Autor:
Takefumi Nosaka
Publikováno v:
Topology and its Applications. 193:1-30
This paper demonstrates a topological meaning of quandle cocycle invariants of links with respect to finite connected quandles $X$, from a perspective of homotopy theory: Specifically, for any prime $\ell$ which does not divide the type of $X$, the $
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6aa13a74955f50696365ff062c6e93b3
https://doi.org/10.1016/j.topol.2015.05.087
https://doi.org/10.1016/j.topol.2015.05.087
Autor:
Takefumi Nosaka
This book surveys quandle theory, starting from basic motivations and going on to introduce recent developments of quandles with topological applications and related topics. The book is written from topological aspects, but it illustrates how esteeme
Autor:
Takefumi Nosaka
Publikováno v:
Algebr. Geom. Topol. 14, no. 5 (2014), 2655-2692
We propose a simple method for producing quandle cocycles from group cocycles by a modification of the Inoue‐Kabaya chain map. Further, we show that, with respect to “universal extension of quandles”, the chain map induces an isomorphism betwee
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4c40f84b5efe67d4ff9c103b3bdeec58
https://doi.org/10.2140/agt.2014.14.2655
https://doi.org/10.2140/agt.2014.14.2655