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

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)
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### References:

 [1] G E Bredon, J W Wood, Non-orientable surfaces in orientable $$3$$-manifolds, Invent. Math. 7 (1969) 83 · Zbl 0175.20504 [2] C Frohman, One-sided incompressible surfaces in Seifert fibered spaces, Topology Appl. 23 (1986) 103 · Zbl 0606.57007 [3] J Hempel, One sided incompressible surfaces in $$3$$-manifolds, Springer (1975) · Zbl 0305.57002 [4] R Rannard, Incompressible surfaces in Seifert fibered spaces, Topology Appl. 72 (1996) 19 · Zbl 0859.57019 [5] J H Rubinstein, One-sided Heegaard splittings of $$3$$-manifolds, Pacific J. Math. 76 (1978) 185 · Zbl 0394.57013 [6] J Stallings, On the loop theorem, Ann. of Math. $$(2)$$ 72 (1960) 12 · Zbl 0094.36103 [7] F Waldhausen, Heegaard-Zerlegungen der $$3$$-Sphäre, Topology 7 (1968) 195 · Zbl 0157.54501
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