Some bounds for the regular genus of PL-manifolds
The regular genus g(M) for a compact connected PL n-manifold M with (possibly empty) boundary \(\partial M\) was defined by \textit{C. Gagliardi} [Proc. Am. Math. Soc. 81, 473-481 (1981; Zbl 0467.57004), and Geom. Dedicata 22, 261-281 (1987; Zbl 0618.57009)]. The authors prove that the genus of non-orientable manifolds is always even. It is also demonstrated that g(M)\(\geq rank \Pi_ 1(M)\) and g(M)\(\geq g(\partial M)\).
scientific article; zbMATH DE number 4149157
scientific article