Three papers on operator algebras in geometric topology

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Focusing on the intersection of geometric topology and operator algebras, this monograph introduces innovative functors that connect topological spaces to operator algebras, aiding in the resolution of complex problems in topology. The first chapter presents new invariants for three-dimensional manifolds derived from operator algebras. The second chapter explores the relationship between homology invariants and K-theory of Cuntz-Krieger algebras. Finally, the third chapter addresses the Harvey conjecture for the mapping class group through noncommutative geometry techniques.