Geodesic
Equivalence of two definitions of the algebraic $K$-theory of spaces
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (1982), pp. 8-12

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We introduce a new construction of the algebraic $K$-functor $AX$ for any topological space $X$. This construction has the origin in the theory of buildings and BN-pairs. Then we prove the equivalence of this construction and that of Waldhausen. 
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     author = {Yu. P. Solov'ev},
     title = {Equivalence of two definitions of the algebraic $K$-theory of spaces},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {8--12},
     publisher = {mathdoc},
     number = {6},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_1982_6_a2/}
}
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Yu. P. Solov'ev. Equivalence of two definitions of the algebraic $K$-theory of spaces. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (1982), pp. 8-12. http://geodesic.mathdoc.fr/item/VMUMM_1982_6_a2/