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pro vyhledávání: '"Yokura, Shoji"'
A stratified space is a topological space equipped with a \emph{stratification}, which is a decomposition or partition of the topological space satisfying certain extra conditions. More recently, the notion of poset-stratified space, i.e., topologica
Externí odkaz:
http://arxiv.org/abs/2407.17690
Autor:
Yokura, Shoji
A simply connected topological space is called \emph{rationally elliptic} if the rank of its total homotopy group and its total (co)homology group are both finite. A well-known Hilali conjecture claims that for a rationally elliptic space its homotop
Externí odkaz:
http://arxiv.org/abs/2407.06548
Autor:
Yokura, Shoji
Publikováno v:
Mathematics Research Reports, Volume 5 (2024), 21-55
For a covariant functor W. Fulton and R. MacPherson defined \emph{an operational bivariant theory} associated to this covariant functor. In this paper we will show that given a contravariant functor one can similarly construct a ``dual" version of an
Externí odkaz:
http://arxiv.org/abs/2306.14516
Autor:
Yokura, Shoji
Publikováno v:
Pure and Applied Mathematics Quarterly, Volume 20, Number 2, 955-1004, 2024
A bi-variant theory $\mathbb B(X,Y)$ defined for a pair $(X,Y)$ is a theory satisfying properties similar to those of Fulton--MacPherson's bivariant theory $\mathbb B(X \xrightarrow f Y)$ defined for a morphism $f:X \to Y$. In this paper, using corre
Externí odkaz:
http://arxiv.org/abs/2207.00269
Autor:
Libgober, Anatoly, Yokura, Shoji
Publikováno v:
Homology, Homotopy and Applications, 24(2) (2022), 93-113
We discuss inequalities between the values of \emph{homotopical and cohomological Poincar\'e polynomials} of the self-products of rationally elliptic spaces. For rationally elliptic quasi-projective varieties, we prove inequalities between the values
Externí odkaz:
http://arxiv.org/abs/2107.11518
Autor:
Libgober, Anatoly, Yokura, Shoji
Publikováno v:
Topology and its Applications, 313 (2022), 1107986
We give a survey on recent results on inequalities between the ranks of homotopy and cohomology groups (resp., graded components of mixed Hodge structures on these groups) of rationally elliptic spaces (resp., quasi-projective varieties which are rat
Externí odkaz:
http://arxiv.org/abs/2107.11520
Autor:
Yamaguchi, Toshihiro, Yokura, Shoji
Publikováno v:
Tbilisi Mathematical Journal, 13(4) (2020), pp. 33-47
In this paper we introduce homological and homotopical Poincar\'e polynomials $P_f(t)$ and $P^{\pi}_f(t)$ of a continuous map $f:X \to Y$ such that if $f:X \to Y$ is a constant map, or more generally, if $Y$ is contractible, then these Poincar\'e pol
Externí odkaz:
http://arxiv.org/abs/2007.01490
Autor:
Yokura, Shoji
Publikováno v:
INTEGERS: Electronic Journal of Combinatorial Number Theory, 20 (2020), Paper #A49, 15pp
Let $\{G_n\}$ be a periodic sequence of integers modulo $m$ and let $\{SG_n\}$ be the partial sum sequence defined by $SG_n:= \sum_{k=0}^nG_k $ (mod $m$). We give a formula for the period of $\{SG_n\}$. We also show that for a generalized Fibonacci s
Externí odkaz:
http://arxiv.org/abs/2006.12002
Autor:
Yokura, Shoji
Publikováno v:
Proc. Japan. Acad. Ser. A, Vol.96 (2020), 28-31
For a simply connected complex algebraic variey $X$, by the mixed Hodge structures $(W_{\bullet}, F^{\bullet})$ and $(\tilde W_{\bullet}, \tilde F^{\bullet})$ of the homology group $H_{*}(X;\mathbb Q)$ and the homotopy groups $\pi_{*}(X)\otimes \math
Externí odkaz:
http://arxiv.org/abs/2003.01976
Autor:
Yokura, Shoji
Publikováno v:
Tbilisi Mathematical Journal, Vol.12, No. 4 (2019), 123--129
The Hilali conjecture claims that a simply connected rationally elliptic space $X$ satisfies the inequality $\operatorname{dim} (\pi_*(X)\otimes \mathbb Q ) \leqq \operatorname{dim} H_*(X;\mathbb Q )$. In this paper we show that for any such space $X
Externí odkaz:
http://arxiv.org/abs/1912.03850