On manifolds homotopy equivalent to the total spaces of S 7 -bundles over S 8

Ajay Raj; Tibor Macko

Archivum Mathematicum (2024)

  • Volume: 060, Issue: 3, page 125-134
  • ISSN: 0044-8753

Abstract

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We calculate the structure sets in the sense of surgery theory of total spaces of bundles over eight-dimensional sphere with fibre a seven-dimensional sphere, in which manifolds homotopy equivalent to the total spaces are organized, and we investigate the question, which of the elements in these structure sets can be realized as such bundles.

How to cite

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Raj, Ajay, and Macko, Tibor. "On manifolds homotopy equivalent to the total spaces of $S^7$-bundles over $S^8$." Archivum Mathematicum 060.3 (2024): 125-134. <http://eudml.org/doc/299435>.

@article{Raj2024,
abstract = {We calculate the structure sets in the sense of surgery theory of total spaces of bundles over eight-dimensional sphere with fibre a seven-dimensional sphere, in which manifolds homotopy equivalent to the total spaces are organized, and we investigate the question, which of the elements in these structure sets can be realized as such bundles.},
author = {Raj, Ajay, Macko, Tibor},
journal = {Archivum Mathematicum},
keywords = {vector bundle; sphere bundle over sphere; microbundle; homotopy equivalence; homeomorphism; surgery; characteristic class},
language = {eng},
number = {3},
pages = {125-134},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {On manifolds homotopy equivalent to the total spaces of $S^7$-bundles over $S^8$},
url = {http://eudml.org/doc/299435},
volume = {060},
year = {2024},
}

TY - JOUR
AU - Raj, Ajay
AU - Macko, Tibor
TI - On manifolds homotopy equivalent to the total spaces of $S^7$-bundles over $S^8$
JO - Archivum Mathematicum
PY - 2024
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 060
IS - 3
SP - 125
EP - 134
AB - We calculate the structure sets in the sense of surgery theory of total spaces of bundles over eight-dimensional sphere with fibre a seven-dimensional sphere, in which manifolds homotopy equivalent to the total spaces are organized, and we investigate the question, which of the elements in these structure sets can be realized as such bundles.
LA - eng
KW - vector bundle; sphere bundle over sphere; microbundle; homotopy equivalence; homeomorphism; surgery; characteristic class
UR - http://eudml.org/doc/299435
ER -

References

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