We present an algorithmic and combinatorial proof of the following well-known theorem, originally proved by Rohlin: `Every closed orientable 3-manifold $M^3$ bounds a simply connected orientable 4-manifold $M^4$.' More precisely, an edge-coloured graph representing $M^4$ is obtained as the final result of a finite and well-determined sequence of `admissible moves', starting from any given edge-coloured graph representing $M^3$.
A combinatorial proof of Rohlin Theorem / Casali, Maria Rita; Gagliardi, Carlo. - In: GEOMETRIAE DEDICATA. - ISSN 0046-5755. - STAMPA. - 64:(3)(1997), pp. 297-310. [10.1023/A:1004992928943]
A combinatorial proof of Rohlin Theorem
CASALI, Maria Rita;GAGLIARDI, Carlo
1997
Abstract
We present an algorithmic and combinatorial proof of the following well-known theorem, originally proved by Rohlin: `Every closed orientable 3-manifold $M^3$ bounds a simply connected orientable 4-manifold $M^4$.' More precisely, an edge-coloured graph representing $M^4$ is obtained as the final result of a finite and well-determined sequence of `admissible moves', starting from any given edge-coloured graph representing $M^3$.
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