Geodesic
Elementary abelian group actions on a product of spaces of cohomology type (a, b)
Filomat, Tome 37 (2023) no. 26, p. 8969

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DOI

Let X n be a finite CW complex with cohomology type (a, b), characterized by an integer n > 1 [20]. In this paper, we show that if G = (Z 2) q acts freely on the product Y = m i=1 X i n , where X i n are finite CW complexes with cohomology type (a, b), a and b are even for every i, then q ≤ m. Moreover, for n even and a = b = 0, we prove that G = (Z 2) q (q ≤ m) is the only finite group which can act freely on Y. These are generalizations of the results which says that the rank of a group acting freely on a space with cohomology type (a, b) where a and b are even, is one and for n even, G = Z 2 is the only finite group which acts freely on spaces of cohomology type (0, 0) [17].
DOI : 10.2298/FIL2326969S
Classification : 57S17, 55T10, 55S10
Keywords: Free action, Leray-Serre spectral sequence, Steenrod square 
Hemant Kumar Singh; Somorjit Singh. Elementary abelian group actions on a product of spaces of cohomology type (a, b). Filomat, Tome 37 (2023) no. 26, p. 8969 . doi: 10.2298/FIL2326969S
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     title = {Elementary abelian group actions on a product of spaces of cohomology type (a, b)},
     journal = {Filomat},
     pages = {8969 },
     year = {2023},
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     doi = {10.2298/FIL2326969S},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2326969S/}
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