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- W2963660130 abstract "We make a detailed study of various (quadratic and linear) Morse-Bott trace functions on the orthogonal groups $O(n)$. We describe the critical loci of the quadratic trace function Tr$(AXBX^T)$ and determine their indices via perfect fillings of tables associated with the multiplicities of the eigenvalues of $A$ and $B$. We give a simplified treatment of T. Frankel's analysis of the linear trace function on $SO(n)$, as well as a combinatorial explanation of the relationship between the mod $2$ Betti numbers of $SO(n)$ and those of the Grassmannians $mathbb{G}(2k,n)$ obtained from this analysis. We review the basic notions of Morse-Bott cohomology in a simple case where the set of critical points has two connected components. We then use these results to give a new Morse-theoretic computation of the mod $2$ Betti numbers of $SO(n)$." @default.
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- W2963660130 date "2019-09-01" @default.
- W2963660130 modified "2023-10-18" @default.
- W2963660130 title "Morse-Bott functions on orthogonal groups" @default.
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- W2963660130 doi "https://doi.org/10.1016/j.topol.2019.07.001" @default.
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