Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-20T06:34:49.796Z Has data issue: false hasContentIssue false
  • English
  • Français

THE COHOMOLOGY RING OF ORBIT SPACES OF FREE $\mathbb{Z}_{2}$-ACTIONS ON SOME DOLD MANIFOLDS

Part of: Fiber spaces and bundles

Published online by Cambridge University Press:  02 February 2018

ANA MARIA M. MORITA Open the ORCID record for ANA MARIA M. MORITA [Opens in a new window] ,
DENISE DE MATTOS Open the ORCID record for DENISE DE MATTOS [Opens in a new window]  and
PEDRO L. Q. PERGHER Open the ORCID record for PEDRO L. Q. PERGHER [Opens in a new window]
ANA MARIA M. MORITA
Affiliation:
Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, CP 668, 13560-970, São Carlos - SP, Brazil email [email protected]
DENISE DE MATTOS
Affiliation:
Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, CP 668, 13560-970, São Carlos - SP, Brazil email [email protected]
PEDRO L. Q. PERGHER*
Affiliation:
Departamento de Matemática, Centro de Ciências Exatas e Tecnologia, Universidade Federal de São Carlos, CP 676, CEP 13565-905, São Carlos - SP, Brazil email [email protected]
*
✉[email protected]
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 determine the possible $\mathbb{Z}_{2}$-cohomology rings of orbit spaces of free actions of $\mathbb{Z}_{2}$ (or fixed point free involutions) on the Dold manifold $P(1,n)$, where $n$ is an odd natural number.

Keywords

Dold manifoldcohomology ringorbit spaceLeray–Serre spectral sequenceBorel fibration

MSC classification

Primary: 57S17: Finite transformation groups
Secondary: 55R20: Spectral sequences and homology of fiber spaces 57S25: Groups acting on specific manifolds
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 2 , April 2018 , pp. 340 - 348
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

References

Borel, A., Seminar on Transformation Groups (Princeton University Press, Princeton, NJ, 1960).Google Scholar
Bredon, G. E., Introduction to Compact Transformation Groups (Academic Press, New York, 1972).Google Scholar
Conner, P. E. and Floyd, E. E., Differentiable Periodic Maps, Ergebnisse Series, 33 (Springer, Berlin–Heidelberg, 1964).Google Scholar
Davis, D. M., ‘Projective product spaces’, J. Topol. 3 (2010), 265–279.CrossRefGoogle Scholar
Dold, A., ‘Erzeugende der Thomschen Algebra N’, Math. Z. 65 (1956), 25–35.Google Scholar
Khare, S. S., ‘On Dold manifolds’, Topology Appl. 33 (1989), 297–307.Google Scholar
McCleary, J., A User’s Guide to Spectral Sequences, 2nd edn (Cambridge University Press, New York, 2001).Google Scholar
Pergher, P. L. Q., Singh, H. K. and Singh, T. B., ‘On Z2 and S1 free actions on spaces of cohomology type (a, b)’, Houston J. Math. 36(1) (2010), 137–146.Google Scholar
Spanier, E. H., Algebraic Topology (McGraw-Hill, New York, 1966).Google Scholar