Geodesic
Cohomology classification of spaces with free S1 and S3-actions
Filomat, Tome 36 (2022) no. 20, p. 7021

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DOI

This paper gives the cohomology classification of finitistic spaces X equipped with free actions of the group G = S 3 and the cohomology ring of the orbit space X/G is isomorphic to the integral cohomology quaternion projective space HP n. We have proved that the integral cohomology ring of X is isomorphic either to S 4n+3 or S 3 × HP n. Similar results with other coefficient groups and for G = S 1 actions are also discussed. As an application, we determine a bound of the index and co-index of cohomology sphere S 2n+1 (resp. S 4n+3) with respect to S 1-actions (resp. S 3-actions).
DOI : 10.2298/FIL2220021K
Classification : 55T10, 57S99
Keywords: Free action, finitistic space, Leray-Serre spectral sequence, Gysin sequence, Euler class 
Anju Kumaria; Hemant Kumar Singha. Cohomology classification of spaces with free S1 and S3-actions. Filomat, Tome 36 (2022) no. 20, p. 7021 . doi: 10.2298/FIL2220021K
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     author = {Anju Kumaria and Hemant Kumar Singha},
     title = {Cohomology classification of spaces with free {S1} and {S3-actions}},
     journal = {Filomat},
     pages = {7021 },
     year = {2022},
     volume = {36},
     number = {20},
     doi = {10.2298/FIL2220021K},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2220021K/}
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