We introduce the concept of generalized handles in (n+1)-colored graphs, and determine many combinatorial and topological properties of them. Then the operations of cancelling and cutting a generalized handle are studied. As a consequence, some decomposition theorems about manifolds are proved. In particular, a graph-theoretical condition is obtained to recognize S^(n-1)-bundles over S^1 as factors of a decomposition of a manifold in connected sum.
Generalized handles in graphs and connected sums of manifolds / Cavicchioli, Alberto. - In: JOURNAL OF GEOMETRY. - ISSN 0047-2468. - STAMPA. - 30:(1987), pp. 69-84.
Generalized handles in graphs and connected sums of manifolds
CAVICCHIOLI, Alberto
1987
Abstract
We introduce the concept of generalized handles in (n+1)-colored graphs, and determine many combinatorial and topological properties of them. Then the operations of cancelling and cutting a generalized handle are studied. As a consequence, some decomposition theorems about manifolds are proved. In particular, a graph-theoretical condition is obtained to recognize S^(n-1)-bundles over S^1 as factors of a decomposition of a manifold in connected sum.
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