1,172 research outputs found
Universal Lefschetz fibrations and Lefschetz cobordisms
We construct universal Lefschetz fibrations, defined in analogy with
classical universal bundles. We also introduce the cobordism groups of
Lefschetz fibrations, and we see how these groups are quotients of the singular
bordism groups via the universal Lefschetz fibrations.Comment: 14 pages; minor revision to match the published versio
Representing Dehn twists with branched coverings
We show that any homologically non-trivial Dehn twist of a compact surface F
with boundary is the lifting of a half-twist in the braid group B_n, with
respect to a suitable branched covering p : F -> B^2. In particular, we allow
the surface to have disconnected boundary. As a consequence, any allowable
Lefschetz fibration on B^2 is a branched covering of B^2 x B^2.Comment: Major revision. It has been added Corollary 3 about the lifting
homomorphism. Are been added also some remarks and are given some other
definitions. There are now 19 figures and 23 page
Branched coverings of and other basic 4-manifolds
We give necessary and sufficient conditions for a 4-manifold to be a branched
covering of , , and , which are expressed in terms of the Betti numbers and the
intersection form of the 4-manifold.Comment: 16 pages, 1 figure, 19 reference
A concave holomorphic filling of an overtwisted contact -sphere
In this paper we prove that the closed -ball admits non-K\"ahler complex
structures with strictly pseudoconcave boundary. Moreover, the induced contact
structure on the boundary -sphere is overtwisted.Comment: 11 pages, 0 figur
A universal ribbon surface in B^4
We construct an orientable ribbon surface F in B^4, which is universal in the
following sense: any compact orientable pl 4-manifold having a handle
decomposition with 0-, 1- and 2-handles can be represented as a cover of B^4
branched over F.Comment: 19 pages, 28 figures, 28 references. LaTeX 2.09 file. Uses:
amstext.sty amscd.sty geom.sty epsf.st
On branched covering representation of 4-manifolds
We provide new branched covering representations for bounded and/or
non-compact 4-manifolds, which extend the known ones for closed 4-manifolds.
Assuming to be a connected oriented PL 4-manifold, our main results are the
following: (1) if is compact with (possibly empty) boundary, there exists a
simple branched cover , where the 's are disjoint PL 4-balls, is the
number of boundary components of ; (2) if is open, there exists a simple
branched cover , where
is the end space of tamely embedded in . In
both cases, the degree and the branching set of can be assumed
to satisfy one of these conditions: (1) and is a properly
self-transversally immersed locally flat PL surface; (2) and is
a properly embedded locally flat PL surface. In the compact (resp. open) case,
by relaxing the assumption on the degree we can have (resp. ) as the
base of the covering. We also define the notion of branched covering between
topological manifolds, which extends the usual one in the PL category. In this
setting, as an interesting consequence of the above results, we prove that any
closed oriented topological 4-manifold is a 4-fold branched covering of .
According to almost-smoothability of 4-manifolds, this branched cover could be
wild at a single point.Comment: 16 pages, 9 figure
- …