Geodesic
Quadratic forms of closed manifolds
Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part IV, Tome 122 (1982), pp. 104-108 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the paper is shown that for any integer unimodular quadratic form and $n=8k+4$ $(k\geqslant1)$ there exists a smooth closed $n$-dimensional manifold with this form. The proof is based on using “plumbing” for construction of smooth closed $3$-connected eight-dimensional manifolds with a given form. 
@article{ZNSL_1982_122_a8,
     author = {O. A. Ivanov},
     title = {Quadratic forms of closed manifolds},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {104--108},
     year = {1982},
     volume = {122},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1982_122_a8/}
}
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O. A. Ivanov. Quadratic forms of closed manifolds. Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part IV, Tome 122 (1982), pp. 104-108. http://geodesic.mathdoc.fr/item/ZNSL_1982_122_a8/