Geodesic
Trace class operators, regulators, and assembly maps in $K$-theory
Documenta mathematica, Tome 19 (2014), pp. 439-455
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Let G be a group and let KH be homotopy algebraic K-theory. We prove that if G satisfies the rational KH isomorphism conjecture for the group algebra L1[G] with coefficients in the algebra of trace-class operators in Hilbert space, then it also satisfies the K-theoretic Novikov conjecture for the group algebra over the integers, and the rational injectivity part of the Farrell-Jones conjecture with coefficients in any number field.
DOI : 10.4171/dm/452
Classification : 19D55, 19F27, 19K99
Mots-clés : Borel regulator, homotopy algebraic K-theory, multiplicative K-theory, trace-class operators 
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     author = {Gisela Tartaglia and Guillermo Corti\~nas},
     title = {Trace class operators, regulators, and assembly maps in $K$-theory},
     journal = {Documenta mathematica},
     pages = {439--455},
     year = {2014},
     volume = {19},
     doi = {10.4171/dm/452},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/452/}
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Gisela Tartaglia; Guillermo Cortiñas. Trace class operators, regulators, and assembly maps in $K$-theory. Documenta mathematica, Tome 19 (2014), pp. 439-455. doi: 10.4171/dm/452

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