Surgery spectral sequence and stratified manifolds

Details Surgery spectral sequence and stratified manifolds Surgery spectral sequence and stratified manifolds

2006-08-29

arxiv.org/abs/math/0608729v1

Trans. Moscow Math. Soc. 67 (2006), 261-288.

Mathematics

Geometric Topology

Trans. Moscow Math. Soc., to appear

Scientific paper

Cappell and Shaneson pointed out in 1978 interesting properties of Browder - Livesay invariants which are similar to differentials in some spectral sequence. Such spectral sequence was constructed in 1991 by Hambleton and Kharshiladze. This spectral sequence is closely related to a problem of realization of elements of Wall groups by normal maps of closed manifolds. The main step of construction of the spectral sequence is an infinite filtration of spectra in which only the first two, as is well-known, have clear geometric sense. The first one is a spectrum $\Bbb L(\pi_1(X))$ for surgery obstruction groups of a manifold $X$ and the second $\Bbb LP_*(F)$ is a spectrum for surgery on a Browder-Livesay manifold pair $Y\subset X$. The geometric sense of the third term of filtration was explained by Muranov, Repov\v{s}, and Spaggiari in 2002. In the present paper we give a geometric interpretation of all spectra of filtration in construction of Hambleton and Kharshiladze. We introduce groups of obstructions to surgery on a system of embeddedd manifolds and prove that spectra which realize these groups coincide with spectra in the filtration of Hambleton and Kharshiladze. We describe algebraic and geometric properties of introduced obstruction groups and their relations to the classical surgery theory. We prove isomorphism between introduced groups and Browder-Quinn $L$-groups of stratified manifolds. We give an application of our results to closed manifold surgery problem and iterated Browder-Livesay invariant.

Affiliated with

Also associated with

No associations

Rating

Surgery spectral sequence and stratified manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Surgery spectral sequence and stratified manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Surgery spectral sequence and stratified manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-334098