Surgery obstruction

In mathematics, specifically in surgery theory, the surgery obstructions define a map θ : N ( X ) → L n ( π 1 ( X ) ) {displaystyle heta colon {mathcal {N}}(X) o L_{n}(pi _{1}(X))} from the normal invariants to the L-groups which is in the first instance a set-theoretic map (that means not necessarily a homomorphism) with the following property when n ≥ 5 {displaystyle ngeq 5} : In mathematics, specifically in surgery theory, the surgery obstructions define a map θ : N ( X ) → L n ( π 1 ( X ) ) {displaystyle heta colon {mathcal {N}}(X) o L_{n}(pi _{1}(X))} from the normal invariants to the L-groups which is in the first instance a set-theoretic map (that means not necessarily a homomorphism) with the following property when n ≥ 5 {displaystyle ngeq 5} : A degree-one normal map ( f , b ) : M → X {displaystyle (f,b)colon M o X} is normally cobordant to a homotopy equivalence if and only if the image θ ( f , b ) = 0 {displaystyle heta (f,b)=0} in L n ( Z [ π 1 ( X ) ] ) {displaystyle L_{n}(mathbb {Z} )} .