arXiv subjects

Daisuke Kishimoto

Publications and source records attributed to Daisuke Kishimoto.

60 records · Page 4Linked to original sources

arXiv2015

Infiniteness of $A_\infty$-types of gauge groups

Let $G$ be a compact connected Lie group and let $P$ be a principal $G$-bundle over $K$. The gauge group of $P$ is the topological group of automorphisms of $P$. For fixed $G$ and $K$, consider all principal $G$-bundles $P$ over $K$. It is proved by Crabb--Sutherland and the second author that the number of $A_n$-types of the gauge groups of $P$ is finite if $n<\infty$ and $K$ is a finite complex. We show that the number of $A_\infty$-types of the gauge groups of $P$ is infinite if $K$ is a sphere and there are infinitely many $P$.

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arXiv2014

$p$-local stable splitting of quasitoric manifolds

We show a homotopy decomposition of $p$-localized suspension $ΣM_{(p)}$ of a quasitoric manifold $M$ by constructing power maps. As an application we investigate the $p$-localized suspension of the projection $π$ from the moment-angle complex onto $M$, from which we deduce its triviality for $p>\dim M/2$. We also discuss non-triviality of $π_{(p)}$ and $Σ^\inftyπ$.

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arXiv2014

Homotopy decomposition of diagonal arrangements

Given a space $X$ and a simplicial complex $K$ with $m$-vertices, the arrangement of partially diagonal subspaces of $X^m$, called the dragonal arrangement, is defined. We decompose the suspension of the diagonal arrangement when $2(dim K + 1) < m$, which generalizes the result of Labassi. As a corollary, we calculate the Euler characteristic of the complement when $X$ is a closed connected manifold.

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arXiv2014

Samelson products in p-regular exceptional Lie groups

The (non)triviality of Samelson products of the inclusions of the spheres into p-regular exceptional Lie groups is completely determined, where a connected Lie group is called p-regular if it has the p-local homotopy type of a product of spheres.

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arXiv2013

Wedge decomposition of polyhedral products

We prove that certain polyhedral products, including the moment-angle complexes, for the Alexander duals of shellable and sequentially Cohen-Macaulay complexes decompose into wedges of explicitly given suspension spaces, which implies the properties of the Stanley-Reisner rings, known as Golod, of theses complexes.

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arXiv2007

Homotopy nilpotency in p-compact groups

A p-compact group is a mod p homotopy theoretical analogue of a compact Lie group. It is determined the homotopy nilpotency class of a p-compact group having the homotopy type of the $p$-completion of the direct product of spheres.

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