## Bordism of two commuting involutions

HTML articles powered by AMS MathViewer

- by Pedro L. Q. Pergher PDF
- Proc. Amer. Math. Soc.
**126**(1998), 2141-2149 Request permission

## Abstract:

In this paper we obtain conditions for a Whitney sum of three vector bundles over a closed manifold, $\varepsilon _{1} \oplus \varepsilon _{2} \oplus \varepsilon _{3} \rightarrow F$, to be the fixed data of a $(Z_{2})^{2}$-action; these conditions yield the fact that if $(\varepsilon _{1} \oplus R) \oplus \varepsilon _{2} \oplus \varepsilon _{3} \rightarrow F$ is the fixed data of a $(Z_{2})^{2}$-action, where $R \rightarrow F$ is the trivial one dimensional bundle, then the same is true for $\varepsilon _{1} \oplus \varepsilon _{2} \oplus \varepsilon _{3} \rightarrow F$. The results obtained, together with techniques previously developed, are used to obtain, up to bordism, all possible $(Z_{2})^{2}$-actions fixing the disjoint union of an even projective space and a point.## References

- A. Borel and F. Hirzebruch,
*Characteristic classes and homogeneous spaces. I*, Amer. J. Math.**80**(1958), 458–538. MR**102800**, DOI 10.2307/2372795 - Czes Kosniowski and R. E. Stong,
*Involutions and characteristic numbers*, Topology**17**(1978), no. 4, 309–330. MR**516213**, DOI 10.1016/0040-9383(78)90001-0 - David C. Royster,
*Involutions fixing the disjoint union of two projective spaces*, Indiana Univ. Math. J.**29**(1980), no. 2, 267–276. MR**563211**, DOI 10.1512/iumj.1980.29.29018 - P. E. Conner and E. E. Floyd,
*Differentiable periodic maps*, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 33, Academic Press, Inc., Publishers, New York; Springer-Verlag, Berlin-Göttingen-Heidelberg, 1964. MR**0176478** - Pedro L. Q. Pergher,
*An equivariant construction*, Proc. Amer. Math. Soc.**119**(1993), no. 1, 319–320. MR**1152991**, DOI 10.1090/S0002-9939-1993-1152991-8 - Pedro L. Q. Pergher,
*Manifolds with $(\textbf {Z}_2)^k$-action*, Proc. Amer. Math. Soc.**106**(1989), no. 4, 1091–1094. MR**969320**, DOI 10.1090/S0002-9939-1989-0969320-1 - Pedro L. Q. Pergher,
*The union of a connected manifold and a point as fixed set of commuting involutions*, Topology Appl.**69**(1996), no. 1, 71–81. MR**1378389**, DOI 10.1016/0166-8641(95)00075-5 - Pedro L. Q. Pergher,
*$(Z_2)^k$-actions fixing a product of spheres and a point*, Canad. Math. Bull.**38**(1995), no. 3, 366–372. MR**1347311**, DOI 10.4153/CMB-1995-053-1 - R. E. Stong,
*Bordism and involutions*, Ann. of Math. (2)**90**(1969), 47–74. MR**242170**, DOI 10.2307/1970681 - R. E. Stong,
*Equivariant bordism and $(Z_{2})^{k}$ actions*, Duke Math. J.**37**(1970), 779–785. MR**271966**, DOI 10.1215/S0012-7094-70-03793-2 - R. E. Stong,
*Involutions fixing projective spaces*, Michigan Math. J.**13**(1966), 445–447. MR**206979**, DOI 10.1307/mmj/1028999602

## Additional Information

**Pedro L. Q. Pergher**- Affiliation: Universidade Federal de São Carlos, Departamento de Matemática, Rodovia Washington Luiz, km. 235, 13.565-905, São Carlos, S.P., Brazil
- Email: pergher@power.ufscar.br
- Received by editor(s): November 7, 1996
- Received by editor(s) in revised form: December 12, 1996
- Additional Notes: The present work was partially supported by CNPq
- Communicated by: Thomas Goodwillie
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**126**(1998), 2141-2149 - MSC (1991): Primary 57R85; Secondary 57R75
- DOI: https://doi.org/10.1090/S0002-9939-98-04356-1
- MathSciNet review: 1451825