Surgery Obstruction
Versandkostenfrei!
Versandfertig in 6-10 Tagen
26,99 €
inkl. MwSt.
PAYBACK Punkte
13 °P sammeln!
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, specifically in surgery theory, the surgery obstructions define a map theta colon mathcal{N} (X) to 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 geq 5:A degree one normal map (f,b) colon M to X is normally cobordant to a homotopy equivalence if and only if the image (f,b) = 0 in L_n (mathbb{Z} [pi_1 (X)])If the ...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, specifically in surgery theory, the surgery obstructions define a map theta colon mathcal{N} (X) to 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 geq 5:A degree one normal map (f,b) colon M to X is normally cobordant to a homotopy equivalence if and only if the image (f,b) = 0 in L_n (mathbb{Z} [pi_1 (X)])If the element (f,b) is zero in the L-group surgery can be done on M to modify f to a homotopy equivalence.Geometrically the reason why this is not always possible is that performing surgery in the middle dimension to kill an element in K_k (tilde M) possibly creates an element in K_{k-1} (tilde M) when n = 2k or in K_{k} (tilde M) when n = 2k + 1. So this possibly destroys what has already been achieved. However, if (f,b) is zero, surgeries can be arranged in such a way that this does not happen.
