Computer Calculation of the Degree of Maps into the Poincaré Homology Sphere
Hayat-Legrand, Claude ; Matveev, Sergei ; Zeischang, Heiner
Experiment. Math., Tome 10 (2001) no. 3, p. 497-508 / Harvested from Project Euclid
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Let $M$ and $P$ be Seifert 3-manifolds. Is there a degree one map $f\colon M \rightarrow P\,$? The problem was completely solved by Hayat-Legrand, Wang, and Zieschang for all cases except when $P$ is the Poincaré homology sphere. We investigate the remaining case by elaborating and implementing a computer algorithm that calculates the degree. As a result, we get an explicit experimental expression for the degree through numerical invariants of the induced homomorphism $f_{\#}\colon \pi_1 (M) \rightarrow \pi_1(P)$.
Publié le : 2001-05-14
Classification:  55M25,  55R55,  20F38 
@article{1069855249,
     author = {Hayat-Legrand, Claude and Matveev, Sergei and Zeischang, Heiner},
     title = {Computer Calculation of the Degree of Maps into the Poincar\'e Homology Sphere},
     journal = {Experiment. Math.},
     volume = {10},
     number = {3},
     year = {2001},
     pages = { 497-508},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1069855249}
}

Hayat-Legrand, Claude; Matveev, Sergei; Zeischang, Heiner. Computer Calculation of the Degree of Maps into the Poincaré Homology Sphere. Experiment. Math., Tome 10 (2001) no. 3, pp.  497-508. http://gdmltest.u-ga.fr/item/1069855249/