Double decker sets of generic surfaces in $3$-space as homology classes
Satoh, Shin
Illinois J. Math., Tome 45 (2001) no. 4, p. 823-832 / Harvested from Project Euclid
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The double decker set $\Gamma$ of a generic map $g:F_0^2\rightarrow M^3$ is the preimage of the singularity of the generic surface $g(F_0)$. If both $F_0$ and $M$ are oriented, then $\Gamma$ is regarded as an oriented 1-cycle in $F_0$, which is shown to be null-homologous if $g(F_0)=0\in H_2(M;{\mathbf Z})$. We also investigate a double decker set of a surface diagram which is a generic surface in ${\mathbf{R}}^3$ with crossing information.
Publié le : 2001-07-15
Classification:  57R45,  57Q37,  57Q45 
@article{1258138153,
     author = {Satoh, Shin},
     title = {Double decker sets of generic surfaces in $3$-space as homology classes},
     journal = {Illinois J. Math.},
     volume = {45},
     number = {4},
     year = {2001},
     pages = { 823-832},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138153}
}

Satoh, Shin. Double decker sets of generic surfaces in $3$-space as homology classes. Illinois J. Math., Tome 45 (2001) no. 4, pp.  823-832. http://gdmltest.u-ga.fr/item/1258138153/