3-manifolds and 4-dimensional surgery

Details 3-manifolds and 4-dimensional surgery 3-manifolds and 4-dimensional surgery

2006-10-25

arxiv.org/abs/math/0610741v1

Mathematics

Geometric Topology

AMS-LaTeX, 4 pages, no figures

Scientific paper

Let $X$ be a connected compact 3-manifold with non-empty boundary. Consider the boundary $M$ of $X\times D^2$. $M$ is a 4-dimensional closed manifold and has the same fundamental group as $X$. Various examples of $X$ are known for which a certain assembly map $A:H_4(X;L)\to L_4(\pi_1(X))$ is injective. For such an $X$ and any CW-spine $B$ of $X$, there is a $UV^1$-map $p:M\to B$. For any $\epsilon>0$, if the surgery obstruction for a TOP normal map $(f,b):N\to M$ vanishes, we can perform surgery on $f$ to change it into a $p^{-1}(\epsilon)$-controlled homotopy equivalence.

Affiliated with

Also associated with

No associations

Rating

3-manifolds and 4-dimensional surgery 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 3-manifolds and 4-dimensional surgery, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and 3-manifolds and 4-dimensional surgery will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-378582