Language：English   Publishing type：Research paper (scientific journal)  

We generalize the box and observable distances to those between metric
measure spaces with group actions, and prove some fundamental properties. As an
application, we obtain an example of a sequence of lens spaces with unbounded
dimension converging to the cone of the infinite-dimensional complex projective
space. Our idea is to use the theory of mass-transport.

arXiv

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Other Link： http://arxiv.org/pdf/2104.00187v2

Language：English   Publishing type：Research paper (scientific journal)   Publisher：Cambridge University Press (CUP)  

We study the topological structure of the space $\mathcal{X}$ of isomorphism classes of metric measure spaces equipped with the box or concentration topologies. We consider the scale-change action of the multiplicative group ${\mathbb{R } }_+$ of positive real numbers on $\mathcal{X}$ , which has a one-point metric measure space, say $*$ , as only one fixed-point. We prove that the ${\mathbb{R } }_+$ -action on $\mathcal{X}_* := \mathcal{X} \setminus \{*\}$ admits the structure of non-trivial and locally trivial principal ${\mathbb{R } }_+$ -bundle over the quotient space. Our bundle ${\mathbb{R } }_+ \to \mathcal{X}_* \to \mathcal{X}_*/{\mathbb{R } }_+$ is a curious example of a non-trivial principal fibre bundle with contractible fibre. A similar statement is obtained for the pyramidal compactification of $\mathcal{X}$ , where we completely determine the structure of the fixed-point set of the ${\mathbb{R } }_+$ -action on the compactification.

DOI： 10.1017/prm.2024.111

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

DOI： 10.1007/s10711-024-00921-3

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Other Link： https://link.springer.com/article/10.1007/s10711-024-00921-3/fulltext.html

Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

DOI： 10.1007/s10711-023-00852-5

arXiv

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Other Link： https://link.springer.com/article/10.1007/s10711-023-00852-5/fulltext.html

Language：English   Publishing type：Research paper (scientific journal)   Publisher：Springer Science and Business Media LLC  

DOI： 10.1007/s12220-021-00773-3

arXiv

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Other Link： https://link.springer.com/article/10.1007/s12220-021-00773-3/fulltext.html

Event date： 2025.3

Language：English   Presentation type：Oral presentation (general)  

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Event date： 2024.6

Language：Japanese   Presentation type：Oral presentation (general)  

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Event date： 2024.1

Language：Japanese   Presentation type：Oral presentation (general)  

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Event date： 2023.6

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