Product formulae for surgery obstructions

The quadratic form E8 and exotic homology manifolds

“…In principle, it is possible to compute (λ, µ) directly from the (4m + 2n)-dimensional symmetric Poincaré complex E 8 ⊗ (C( T n ), φ). In practice, we shall use the almost symmetric form surgery product formula of Clauwens [7,5,6], which is the analogue…”

“…In principle, it is possible to compute (λ, µ) directly from the (4m + 2n)-dimensional symmetric Poincaré complex E 8 ⊗ (C( T n ), φ). In practice, we shall use the almost symmetric form surgery product formula of Clauwens [7,5,6], which is the analogue for symmetric Poincaré complexes of the instant surgery obstruction of Section 3. We establish a product formula for almost symmetric forms which will be used in Section 7 to obtain an almost (−1) n -symmetric form for T 2n of rank 2 n 2n n , and hence a representative (−1) n -quadratic form for σ * (f , b) ∈ L 4m+2n (Z[Z 2n ]) of rank 2 n+3 8 2n n .…”