Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-25T07:12:52.632Z Has data issue: false hasContentIssue false
  • English
  • Français

ON SERRE MICROFIBRATIONS AND A LEMMA OF M. WEISS

Published online by Cambridge University Press:  20 March 2017

GEORGE RAPTIS
GEORGE RAPTIS*
Affiliation:
Universität Regensburg, Fakultät für Mathematik, 93040 Regensburg, Germany e-mail: georgios.raptis@ur.de
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We show that every fibrewise map from a Serre microfibration to a Serre fibration is n-connected if it is fibrewise n-connected. This generalises a result of M. Weiss and related results by Bökstedt–Madsen and Galatius–Randal–Williams. We also discuss an application to configuration spaces.

Keywords

55R6555R7055R80
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 59 , Issue 3 , September 2017 , pp. 649 - 657
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

REFERENCES

1. Bökstedt, M. and Madsen, Ib, The cobordism category and Waldhausen's K-theory, in An alpine expedition through algebraic topology, Contemporary Mathematics 617, (Amer. Math. Soc., Providence, RI, 2014), 39–80.Google Scholar
2. Christenson, C. O. and Osborne, R. P., Pointlike subsets of a manifold, Pacific J. Math. 24 (1968), 431–435.Google Scholar
3. Galatius, S. and Randal-Williams, O., Homological stability for moduli spaces of high dimensional manifolds. I, arXiv:1403.2334.Google Scholar
4. Lacher, R. C., Cell-like mappings. I, Pacific J. Math. 30 (1969), 717–731.Google Scholar
5. Lacher, R. C., Cell-like spaces, Proc. Amer. Math. Soc. 20 (1969), 598–602.Google Scholar
6. McMillan, D. R. Jr., A criterion for cellularity in a manifold, Ann. of Math. 79 (2) (1964), 327–337.Google Scholar
7. Mitchell, W. J. R. and Repovš, D., The topology of cell-like mappings, in Conference on Differential Geometry and Topology (Sardinia, 1988), Rend. Sem. Fac. Sci. Univ. Cagliari 58 (1988), 265–300.Google Scholar
8. Raptis, G., Some remarks on configuration spaces, Proc. Amer. Math. Soc. 139 (5) (2011), 1879–1887.Google Scholar
9. Repovš, D., A criterion for cellularity in a topological 4-manifold, Proc. Amer. Math. Soc. 100 (3) (1987), 564–566.Google Scholar
10. Weiss, M., What does the classifying space of a category classify?, Homology Homotopy Appl. 7 (1) (2005), 185–195.Google Scholar