Abstract
The main aim of this paper is to compute the index and the nullity of the identity map of $S^n\times S^m$ and $S^n\times T^m$. In order to obtain this we establish a rather general result on the spectrum of the Hodge-Laplacian on $k$-forms on a product manifold, which could prove useful in other contexts.
Citation
Ali Fardoun. Andrea Ratto. "On the second variation of the identity map of a product manifold." Tohoku Math. J. (2) 52 (2) 235 - 249, 2000. https://doi.org/10.2748/tmj/1178224608
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