Geodesic
Lefschetz Numbers for C*-Algebras
Canadian mathematical bulletin, Tome 54 (2011) no. 1, pp. 82-99

Voir la notice de l'article provenant de la source Cambridge University Press

Using Poincaré duality, we obtain a formula of Lefschetz type that computes the Lefschetz number of an endomorphism of a separable nuclear ${{C}^{*}}$ -algebra satisfying Poincaré duality and the Kunneth theorem. (The Lefschetz number of an endomorphism is the graded trace of the induced map on $\text{K}$ -theory tensored with $\mathbb{C}$ , as in the classical case.) We then examine endomorphisms of Cuntz–Krieger algebras ${{O}_{A}}$ . An endomorphism has an invariant, which is a permutation of an infinite set, and the contracting and expanding behavior of this permutation describes the Lefschetz number of the endomorphism. Using this description, we derive a closed polynomial formula for the Lefschetz number depending on the matrix A and the presentation of the endomorphism.
DOI : 10.4153/CMB-2010-084-5
Mots-clés : 19K35, 46L80 
Emerson, Heath. Lefschetz Numbers for C*-Algebras. Canadian mathematical bulletin, Tome 54 (2011) no. 1, pp. 82-99. doi: 10.4153/CMB-2010-084-5
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