We construct a genus 2 crystallization G of the complex projective plane CP^2, whose associated pseudocomplex is composed by five vertices, ten edges, twenty triangles, twenty tetrahedra and eight 4-simplexes. This is proved to be the most "economical" pseudodissection of CP^2. Moreover, by performing the "connectred sum" of two copies of G, we obtain a genus 4 crystallization of the twisted 2-sphere bundle over S^2.
On the genus of the complex projective plane / Gagliardi, Carlo. - In: AEQUATIONES MATHEMATICAE. - ISSN 0001-9054. - STAMPA. - 37:(1989), pp. 130-140.
On the genus of the complex projective plane
GAGLIARDI, Carlo
1989
Abstract
We construct a genus 2 crystallization G of the complex projective plane CP^2, whose associated pseudocomplex is composed by five vertices, ten edges, twenty triangles, twenty tetrahedra and eight 4-simplexes. This is proved to be the most "economical" pseudodissection of CP^2. Moreover, by performing the "connectred sum" of two copies of G, we obtain a genus 4 crystallization of the twisted 2-sphere bundle over S^2.Pubblicazioni consigliate
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