One-sided Heegaard splittings of \(\mathbb R{\text P}^3\). (English) Zbl 1133.57005

Bartolini, Loretta; Rubinstein, J. Hyam

Algebr. Geom. Topol. 6, 1319-1330 (2006).

Summary: Using basic properties of one-sided Heegaard splittings, a direct proof that geometrically compressible one-sided splittings of \(\mathbb R{\text P}^3\) are stabilised is given. The argument is modelled on that used by Waldhausen to show that two-sided splittings of \(S^3\) are standard.

MSC:

57M27	Invariants of knots and \(3\)-manifolds (MSC2010)
57N10	Topology of general \(3\)-manifolds (MSC2010)

Keywords:

one-sided Heegaard splitting; geometrically compressible

References:

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