Formulae for surgery obstructions

Analytic surgery and gluing formulae for determinants

Projective Surgery Obstructions on Closed Manifolds

paper we answer the analogous questions (i) (iii) about the image ch(~,w) of C h in LP(~,w). These groups are the geometric surgery n n n obstruction groups of Maumary [M] or Taylor IT] ; algebraically they are L-groups of quadratic forms on projective (instead of free) Z~ modules [RI]. The appropriate version of (ii) is then to ask for i 1 invariants detecting o(f x id) where f x id: M x S ÷ N...

Surgery Obstructions on Closed Manifolds and the Inertia Subgroup

The Wall surgery obstruction groups have two interesting geometrically defined subgroups, consisting of the surgery obstructions between closed manifolds, and the inertial elements. We show that the inertia group In+1(π,w) and the closed manifold subgroup Cn+1(π,w) are equal in dimensions n+1 ≥ 6, for any finitely-presented group π and any orientation character w : π → Z/2. This answers a quest...

Evaluation of Odd-dimensional Surgery Obstructions with Finite Fundamental Group

THROUGHOUT the decade following the publication of C.T.C. Walls book, Surgery on Compact Manifolds, there was a tremendous effort on the part of many mathematicians to compute the algebraic L-groups L,(Zn) for finite groups TL. Two noteworthy results were Bak’s theorem that Lzi+ 1 (Zrc) is zero when 7c has odd order, and Wall’s result that Lsi(Z7c) is detected by multisignatures and the classic...

Obstructions for simple embeddings

Suppose that K ⊆ G is a graph embedded in some surface and F is a face of K with singular branches e and f such that F ∪ ∂F is homeomorphic to the torus minus an open disk. An embedding extension of K to G is a simple embedding if each K-bridge embedded in F is attached to at most one appearance of e and at most one appearance of f on ∂F . Combinatorial structure of minimal obstructions for exi...