Summary
We determine bounds for the regular genus of any 4-manifold, which is a product of \(\mathbb{S}^1 \) by a closed 3-manifold, or a product of two closed surfaces. This is done by an explicit construction of a graph representing the manifold, and by finding a minimal regular imbedding of it.
Sunto
Determiniamo una limitazione del genere regolare di una 4-varieta prodotto di \(\mathbb{S}^1 \) per una 3-varieta chiusa, o prodotto di due superficie chiuse, costruendo esplicitamente un grafo che la rappresenta, e trovandone un'immersione regolare minimale.
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This work was performed under the auspieces of the G.N.S.A.G.A. of the C.N.R. (National Research Council) of Italy.
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Ferri, M., Gagliardi, C. On the genus of 4-dimensional products of manifolds. Geom Dedicata 13, 331–345 (1982). https://doi.org/10.1007/BF00148238
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DOI: https://doi.org/10.1007/BF00148238