Geodesic
Splitting homotopy equivalences along a~one-sided submanifold of codimension one
Izvestiya. Mathematics , Tome 30 (1988) no. 2, pp. 185-215.

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An algebraic construction is given for the group of obstructions to splitting homotopy equivalences along a one-sided submanifold of codimension one. Bibliography: 7 titles. 
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P. M. Akhmet'ev. Splitting homotopy equivalences along a~one-sided submanifold of codimension one. Izvestiya. Mathematics , Tome 30 (1988) no. 2, pp. 185-215. http://geodesic.mathdoc.fr/item/IM2_1988_30_2_a0/

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