arXiv subjects

Carlo Gagliardi

Publications and source records attributed to Carlo Gagliardi.

4 recordsLinked to original sources

arXiv2020

Crystallizations of compact 4-manifolds minimizing combinatorially defined PL-invariants

The present paper is devoted to present a unifying survey about some special classes of crystallizations of compact PL $4$-manifolds with empty or connected boundary, called {\it semi-simple} and {\it weak semi-simple crystallizations}, with a particular attention to their properties of minimizing combinatorially defined PL-invariants, such as the {\it regular genus}, the {\it Gurau degree}, the {\it gem-complexity} and the {\it (gem-induced) trisection genus}. The main theorem, yielding a summarizing result on the topic, is an original contribution. Moreover, in the present paper the additivity of regular genus with respect to connected sum is proved to hold for all compact $4$-manifolds with empty or connected boundary which admit weak semi-simple crystallizations.

math.GT↗

arXiv2011

Rigid gems in dimension n

We extend to dimension $n \geq 3$ the concept of $ρ$-pair in a coloured graph and we prove the existence theorem for minimal rigid crystallizations of handle-free, closed $n$-manifolds.

math.GT↗

arXiv2009

A census of genus two 3-manifolds up to 42 coloured tetrahedra

We improve and extend to the non-orientable case a recent result of Karabas, Malicki and Nedela concerning the classification of all orientable prime 3-manifolds of Heegaard genus two, triangulated with at most 42 coloured tetrahedra.

math.GT↗

arXiv2007

Nonorientable 3-manifolds admitting coloured triangulations with at most 30 tetrahedra

We present the census of all non-orientable, closed, connected 3-manifolds admitting a rigid crystallization with at most 30 vertices. In order to obtain the above result, we generate, manipulate and compare, by suitable computer procedures, all rigid non-bipartite crystallizations up to 30 vertices.

math.GT↗