Abstract.
We calculate explicitly the equivariant Ray-Singer torsion for all symmetric spaces \(G/K\) of compact type with respect to the action of \(G\). We show that it equals zero except for the odd-dimensional Graßmannians and the space \(\vec{SU}(3)/\vec{SO}(3)\). As a corollary, we classify up to diffeomorphism all isometries of these spaces which are homotopic to the identity; also, we classify their quotients by finite group actions up to homeomorphism.
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Received: 31 May 1995 / In revised form: 9 January 1996
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Köhler, K. Equivariant Reidemeister torsion on symmetric spaces . Math Ann 307, 57–69 (1997). https://doi.org/10.1007/s002080050022
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DOI: https://doi.org/10.1007/s002080050022