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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 anamariamathiasmorita@gmail.com
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 deniseml@icmc.usp.br
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 pergher@dm.ufscar.br
*
✉pergher@dm.ufscar.br
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Abstract

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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. 

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