Z2k–actions fixing RP²∪RPeven
Algebraic and Geometric Topology, Tome 7 (2007) no. 1, pp. 29-45
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This paper determines, up to equivariant cobordism, all manifolds with Z2k–action whose fixed point set is ℝ P2∪ℝ Pn, where n > 2 is even.

DOI : 10.2140/agt.2007.7.29
Keywords: involution, group action, fixed data, property H, equivariant cobordism class, characteristic number, projective space bundle, Steenrod operation, Conner's formula, s–class

de Oliveira, Rogério  1   ; Pergher, Pedro  2   ; Ramos, Adriana  2

1 Departamento de Ciências Exatas, Universidade Federal de Mato Grosso do Sul, Caixa Postal 210, Três Lagoas, MS 79603-011, Brazil
2 Departamento de Matemática, Universidade Federal de São Carlos, Caixa Postal 676, São Carlos, SP 13565-905, Brazil
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de Oliveira, Rogério; Pergher, Pedro; Ramos, Adriana. Z2k–actions fixing RP²∪RPeven. Algebraic and Geometric Topology, Tome 7 (2007) no. 1, pp. 29-45. doi: 10.2140/agt.2007.7.29

[1] J M Boardman, On manifolds with involution, Bull. Amer. Math. Soc. 73 (1967) 136

[2] P E Conner, The bordism class of a bundle space, Michigan Math. J. 14 (1967) 289

[3] P E Conner, Differentiable periodic maps, Lecture Notes in Mathematics 738, Springer (1979)

[4] P E Conner, E E Floyd, Differentiable periodic maps, Ergebnisse der Mathematik und ihrer Grenzgebiete 33, Academic Press (1964)

[5] P E Conner, E E Floyd, Fibring within a cobordism class, Michigan Math. J. 12 (1965) 33

[6] D Hou, B Torrence, Involutions fixing the disjoint union of odd-dimensional projective spaces, Canad. Math. Bull. 37 (1994) 66

[7] D Hou, B Torrence, Involutions fixing the disjoint union of copies of even projective space, Acta Math. Sinica $($N.S.$)$ 12 (1996) 162

[8] C Kosniowski, R E Stong, Involutions and characteristic numbers, Topology 17 (1978) 309

[9] Z Lü, Involutions fixing $\mathbb{R}\mathbb{P}^{\mathrm{odd}}{\sqcup}P(h,i)$ I, Trans. Amer. Math. Soc. 354 (2002) 4539

[10] Z Lü, Involutions fixing $\mathbb{R}\mathbb{P}^{\mathrm{odd}}{\sqcup}P(h,i)$ II, Trans. Amer. Math. Soc. 356 (2004) 1291

[11] P L Q Pergher, Involutions fixing an arbitrary product of spheres and a point, Manuscripta Math. 89 (1996) 471

[12] P L Q Pergher, $(Z_2)^k$–actions whose fixed data has a section, Trans. Amer. Math. Soc. 353 (2001) 175

[13] P L Q Pergher, R De Oliveira, Commuting involutions whose fixed point set consists of two special components, preprint,

[14] P L Q Pergher, R De Oliveira, $Z_2^k$–actions with a special fixed point set, Fund. Math. 186 (2005) 97

[15] P L Q Pergher, R E Stong, Involutions fixing $(\mathrm{point}){\cup}F^n$, Transform. Groups 6 (2001) 79

[16] D C Royster, Involutions fixing the disjoint union of two projective spaces, Indiana Univ. Math. J. 29 (1980) 267

[17] R E Stong, Involutions fixing projective spaces, Michigan Math. J. 13 (1966) 445

[18] R E Stong, Involutions fixing products of circles, Proc. Amer. Math. Soc. 119 (1993) 1005

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