1,720,970 research outputs found
Representing Dehn twists with branched coverings
No full textWe show that any homologically non-trivial Dehn twist of a compact surface with boundary is the lifting of a half-twist in the braid
group , with respect to a suitable branched covering . In particular, we allow the surface to have disconnected boundary. As a consequence, any allowable Lefschetz fibration on is a branched covering of
On Stiefel's parallelizability of 3-manifolds
Full text linkWe give a new elementary proof of the parallelizability of closed orientable 3-manifolds. We use as the main tool the fact that any such manifold admits a Heegaard splitting
Universal Lefschetz fibrations and Lefschetz cobordisms
No full textWe construct universal Lefschetz fibrations, that are defined in analogy with the classical universal bundles. We also introduce the cobordism groups of Lefschetz fibrations, and we see how these groups are quotient of the singular bordism groups via the universal Lefschetz fibrations
Universal Lefschetz fibrations over bounded surfaces
No full textIn analogy with the vector bundle theory we define universal and strongly universal Lefschetz fibrations over bounded surfaces. After giving a characterization of these fibrations we construct very special strongly universal Lefschetz fibrations when the fiber is the torus or an orientable surface with connected boundary and the base surface is the disk. As a by-product we also get some immersion results for 4-dimensional 2-handlebodies
Non-Kähler complex structures on \mathbbR^4, II
No full textWe follow our study of non-Kähler complex structures on R4 that we defined in our previous paper. We prove that these complex surfaces do not admit any smooth complex compactification. Moreover, we give an explicit description of their meromorphic functions. We also prove that the Picard groups of these complex surfaces are uncountable, and give an explicit description of the canonical bundle. Finally, we show that any connected non-compact oriented 4-manifold admits complex structures without Kähler metrics
On codimension-1 submanifolds of the real and complex projective space
Full text linkInspired by the analogous result in the algebraic setting (Theorem1) we show (Theorem2) that the product M × RP^n of a closed and orientable topological manifold M with the n-dimensional real projective space cannot be embedded into RP^(m+n+1) for all even n > m
A universal ribbon surface in B^4
No full textWe 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
On embeddings of almost complex manifolds in almost complex Euclidean spaces
Full text linkWe prove that any almost complex manifold can be almost holomorphically embedded in an Euclidean space w.r.t. a suitable almost complex structure defined on the whole Euclidean spac
- …
