arXiv subjects

Kazuki Kurimoto

Publications and source records attributed to Kazuki Kurimoto.

4 recordsLinked to original sources

arXiv2020

Cohomological rigidity for Fano Bott manifolds

In the present paper, we characterize Fano Bott manifolds up to diffeomorphism in terms of three operations on matrix. More precisely, we prove that given two Fano Bott manifolds $X$ and $X'$, the following conditions are equivalent: (1) the upper triangular matrix associated to $X$ can be transformed into that of $X'$ by those three operations; (2) $X$ and $X'$ are diffeomorphic; (3) the integral cohomology rings of $X$ and $X'$ are isomorphic as graded rings. As a consequence, we affirmatively answer the cohomological rigidity problem for Fano Bott manifolds.

math.AT↗

arXiv2020

Cohomological rigidity for toric Fano manifolds of small dimensions or large Picard numbers

The cohomological rigidity problem for toric manifolds asks whether toric manifolds are diffeomorphic (or homeomorphic) if their integral cohomology rings are isomorphic. Many affirmative partial solutions to the problem have been obtained and no counterexample is known. In this paper, we study the diffeomorphism classification of toric Fano $d$-folds with $d=3,4$ or with Picard number $\ge 2d-2$. In particular, we show that those manifolds except for two toric Fano $4$-folds are diffeomorphic if their integral cohomology rings are isomorphic. The exceptional two toric Fano $4$-folds (their ID numbers are 50 and 57 on a list of Øbro) have isomorphic cohomology rings and their total Pontryagin classes are preserved under an isomorphism between their cohomology rings, but we do not know whether they are diffeomorphic or homeomorphic.

math.AT↗

arXiv2020

Feedback game on $3$-chromatic Eulerian triangulations of surfaces

In this paper, we study the feedback game on $3$-chromatic Eulerian triangulations of surfaces. We prove that the winner of the game on every $3$-chromatic Eulerian triangulation of a surface all of whose vertices have degree $0$ modulo $4$ is always fixed. Moreover, we also study the case of $3$-chromatic Eulerian triangulations of surfaces which have at least two vertices whose degrees are $2$ modulo $4$, and in particular, we determine the winner of the game on a concrete class of such graphs, called an octahedral path.

cs.DM↗

arXiv2019

Permutations with small maximal $k$-consecutive sums

Let $n$ and $k$ be positive integers with $n>k$. Given a permutation $(π_1,\ldots,π_n)$ of integers $1,\ldots,n$, we consider $k$-consecutive sums of $π$, i.e., $s_i:=\sum_{j=0}^{k-1}π_{i+j}$ for $i=1,\ldots,n$, where we let $π_{n+j}=π_j$. What we want to do in this paper is to know the exact value of $$\mathrm{msum}(n,k):=\min\left\{\max\{s_i : i=1,\ldots,n\} -\frac{k(n+1)}{2}: π\in S_n\right\},$$ where $S_n$ denotes the set of all permutations of $1,\ldots,n$. In this paper, we determine the exact values of $\mathrm{msum}(n,k)$ for some particular cases of $n$ and $k$. As a corollary of the results, we obtain $\mathrm{msum}(n,3)$, $\mathrm{msum}(n,4)$ and $\mathrm{msum}(n,6)$ for any $n$.

math.CO↗