Jaco, William; Rubinstein, J. Hyam PL equivariant surgery and invariant decompositions of 3-manifolds. (English) Zbl 0682.57005 Adv. Math. 73, No. 2, 149-191 (1989). Normal surface theory was introduced by W. Haken to show the existence of hierarchies for certain 3-manifolds M (“Haken-manifolds”). The authors study least weight surfaces, i.e. normal surfaces with minimal intersections with the 1-skeleton of a fixed triangulation of M. The main applications are constructive PL proofs of results which were previously obtained by Meeks-Yau via minimal surface theory. Specifically, let G be a group of simplicial homeomorphisms of M. The authors give PL proofs for (1) the Equivariant Sphere Theorem, (2) the existence of a G-invariant prime decomposition of M (if G is finite and M has no closed 1-handles), (3) the existence of a G-invariant characteristic submanifold V of a Haken-manifold M (if G is finite and M is not a torus bundle over \(S^ 1\) with V a neighborhood of the fiber). Reviewer: W.Heil Cited in 21 Documents MSC: 57N10 Topology of general \(3\)-manifolds (MSC2010) 57S17 Finite transformation groups 57S15 Compact Lie groups of differentiable transformations Keywords:hierarchies; Haken-manifolds; least weight surfaces; normal surfaces; Equivariant Sphere Theorem; G-invariant prime decomposition; G-invariant characteristic submanifold × Cite Format Result Cite Review PDF Full Text: DOI References: [1] M. J. Dunwoody; M. J. Dunwoody · Zbl 0592.57005 [2] Edmonds, A., A topological proof of the equivariant Dehn’s lemma, Trans. Amer. Math. Soc., 297, 605-615 (1986) · Zbl 0605.57004 [3] Epstein, D. B.A, Projective planes in 3-manifolds, (Proc. London Math. Soc., 11 (1961)), 469-484 · Zbl 0111.18801 [4] Freedman, M.; Hass, J.; Scott, P., Least area incompressible surfaces in 3-manifolds, Invent. 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