Constructing infinitely many smooth structures on small 4-manifolds

Details Constructing infinitely many smooth structures on small 4-manifolds Constructing infinitely many smooth structures on small 4-manifolds

2007-03-16

arxiv.org/abs/math/0703480v2

Mathematics

Geometric Topology

23 pages, 3 figures

Scientific paper

The purpose of this article is twofold. First we outline a general construction scheme for producing simply-connected minimal symplectic 4-manifolds with small Euler characteristics. Using this scheme, we illustrate how to obtain irreducible symplectic 4-manifolds homeomorphic but not diffeomorphic to $\CP#(2k+1)\CPb$ for $k = 1,...,4$, or to $3\CP# (2l+3)\CPb$ for $l =1,...,6$. Secondly, for each of these homeomorphism types, we show how to produce an infinite family of pairwise nondiffeomorphic nonsymplectic 4-manifolds belonging to it. In particular, we prove that there are infinitely many exotic irreducible nonsymplectic smooth structures on $\CP#3\CPb$, $3\CP#5\CPb$ and $3\CP#7\CPb$.

Affiliated with

Also associated with

No associations

Rating

Constructing infinitely many smooth structures on small 4-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 Constructing infinitely many smooth structures on small 4-manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Constructing infinitely many smooth structures on small 4-manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-679918