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A coarse Mayer-Vietoris principle. (English) Zbl 0792.55001
The second author has introduced [Mem. Am. Math. Soc. 497 (1993; Zbl 0780.58043)] a cohomology theory, coarse cohomology, for a category of metric spaces, whose examples are complete non compact Riemannian manifolds and groups with word metric. He used this theory to recover and generalize the results of Gromov-Lawson.
In the present note, the authors show that in suitable cases, one gets a Mayer-Vietoris sequence in coarse cohomology and also in the $$K$$-theory of the $$C^*$$-algebra generated by locally compact operators with finite propagation. The last proposition is a verification of the Baum-Connes conjecture in coarse geometry.

##### MSC:
 55N99 Homology and cohomology theories in algebraic topology 19K56 Index theory
##### Keywords:
coarse cohomology; Mayer-Vietoris sequence; $$K$$-theory
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##### References:
 [1] Spanier, Algebraic topology (1966) [2] Higson, J. Functional Anal. [3] Milnor, Pacific J. Math. 12 pp 337– (1962) · Zbl 0114.39604 · doi:10.2140/pjm.1962.12.337 [4] Pedersen, Springer Lecture Notes in Mathematics 1126 pp 306– (1985)
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