222 research outputs found
Homologous Non-isotopic Symplectic Tori in Homotopy Rational Elliptic Surfaces
Let E(1)_K denote the closed 4-manifold that is homotopy equivalent (hence
homeomorphic) to the rational elliptic surface E(1) and is obtained by
performing Fintushel-Stern knot surgery on E(1) using a knot K in S^3. We
construct an infinite family of homologous non-isotopic symplectic tori
representing a primitive homology class in E(1)_K when K is any nontrivial
fibred knot in S^3. We also show how these tori can be non-isotopically
embedded as homologous symplectic submanifolds in other symplectic 4-manifolds.Comment: 8 pages, 2 figure
Constructing infinitely many smooth structures on small 4-manifolds
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 , or to 3\CP# (2l+3)\CPb
for . 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.Comment: 23 pages, 3 figure
Homologous non-isotopic symplectic tori in a K3-surface
For each member of an infinite family of homology classes in the K3-surface
E(2), we construct infinitely many non-isotopic symplectic tori representing
this homology class. This family has an infinite subset of primitive classes.
We also explain how these tori can be non-isotopically embedded as homologous
symplectic submanifolds in many other symplectic 4-manifolds including the
elliptic surfaces E(n) for n>2.Comment: 15 pages, 9 figures; v2: extended the main theorem, gave a second
construction of symplectic tori, added a figure, added/updated references,
minor changes in figure
Reverse engineering small 4-manifolds
We introduce a general procedure called `reverse engineering' that can be
used to construct infinite families of smooth 4-manifolds in a given
homeomorphism type. As one of the applications of this technique, we produce an
infinite family of pairwise nondiffeomorphic 4-manifolds homeomorphic to
CP^2#3(-CP^2).Comment: 13 pages, 2 figures. This is the final version published in AGT,
volume 7 (2007), pp. 2103-2116
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