Geodesic
Bordism groups of Poincare $E_\infty$-coalgebras and symmetric $L$-groups
Sbornik. Mathematics, Tome 186 (1995) no. 7, pp. 1023-1055

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A Poincare $E_\infty$-coalgebra construction over involutive algebras is introduced in this paper. Various types of bordism between Poincare $E_\infty$-coalgebras are defined and the relations between the corresponding bordism groups are studied. It is shown in particular that the Thom bordism groups of closed non-oriented smooth manifolds and the rational Wall groups of a unitary group have a common algebraic origin, that is, they are obtained by the same construction considered over the fields $\mathbb Z/2$ and $\mathbb Q$, respectively. 
@article{SM_1995_186_7_a6,
     author = {S. V. Lapin},
     title = {Bordism groups of {Poincare} $E_\infty$-coalgebras and symmetric $L$-groups},
     journal = {Sbornik. Mathematics},
     pages = {1023--1055},
     publisher = {mathdoc},
     volume = {186},
     number = {7},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_186_7_a6/}
}
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S. V. Lapin. Bordism groups of Poincare $E_\infty$-coalgebras and symmetric $L$-groups. Sbornik. Mathematics, Tome 186 (1995) no. 7, pp. 1023-1055. http://geodesic.mathdoc.fr/item/SM_1995_186_7_a6/