Self-closeness numbers of finite cell complexes

Nobuyuki Oda; Toshihiro Yamaguchi

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arXiv · 1910.10834

Self-closeness numbers of finite cell complexes

Nobuyuki Oda·Toshihiro Yamaguchi

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Abstract

We reformulate the inequalities among self-closeness numbers of spaces in cofibrations making use of homology dimension and show that the self-closeness number of a space is less than or equal to the homology dimension of the space. Then we prove a relation of self-closeness numbers and the connectivity for manifolds satisfying Poincar\'{e} duality. On the other hand we determine the self-closeness numbers of the real projective spaces, lens spaces and a cell complex defined by Mimura and Toda. Moreover, making use of the models of Sullivan and Quillen, we show several properties of self-closeness number for finite cell complexes, and rational examples are udied to obtain some precise results. Finally, we prove relations among self-closeness numbers defined by homotopy groups, homology groups and cohomology groups.

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BibTeX RIS

Nobuyuki Oda, Toshihiro Yamaguchi. 2019-10-23. Self-closeness numbers of finite cell complexes. https://arxiv.org/abs/1910.10834

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