Geodesic
Extension of the Hermitian $K$-theory functor
Sbornik. Mathematics, Tome 198 (2007) no. 8, pp. 1145-1163

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A new construction of symmetric non-commutative signature of non-simply-connected topological manifolds is proposed based on the natural definition of homology and cohomology of a topological manifold using the singular chain and cochain complexes. Bibliography: 5 titles. 
@article{SM_2007_198_8_a4,
     author = {P. S. Popov},
     title = {Extension of the {Hermitian} $K$-theory functor},
     journal = {Sbornik. Mathematics},
     pages = {1145--1163},
     publisher = {mathdoc},
     volume = {198},
     number = {8},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2007_198_8_a4/}
}
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P. S. Popov. Extension of the Hermitian $K$-theory functor. Sbornik. Mathematics, Tome 198 (2007) no. 8, pp. 1145-1163. http://geodesic.mathdoc.fr/item/SM_2007_198_8_a4/