Related papers: Orthogonal 2-sphere basis of stable 4-sphere

Based on Morse theory for the energy functional on path spaces we develop a deformation theory for mapping spaces of spheres into orthogonal groups. This is used to show that these mapping spaces are weakly homotopy equivalent, in a stable…

We identify Le Potier's moduli spaces of limit stable pairs $(F,s)$, where $F$ is a 2-dimensional sheaf on a nonsingular projective 4-fold $X$ and $s \in H^0(F)$, with the moduli spaces of polynomial stable 2-term complexes in derived…

Main Theorem: Spaces of r-branch point 3-cycle covers, degree n or Galois of degree n!/2 have one (resp. two) component(s) if r=n-1 (resp. r\ge n). Improves Fried-Serre on deciding when sphere covers with odd-order branching lift to…

We show that there exists an algorithm that takes as input two closed, simply connected, topological 4-manifolds and decides whether or not these 4-manifolds are homeomorphic. In particular, we explain in detail how closed, simply…

For a given branched covering between closed connected surfaces, there are several easy relations one can establish between the Euler characteristics of the surfaces, their orientability, the total degree, and the local degrees at the…

When two smooth manifold bundles over the same base are fiberwise tangentially homeomorphic, the difference is measured by a homology class in the total space of the bundle. We call this the relative smooth structure class. Rationally and…

We consider codimension 2 sphere congruences in pseudo-conformal geometry that are harmonic with respect to the conformal structure of an orthogonal surface. We characterise the orthogonal surfaces of such congruences as either $S$-Willmore…

We present a pair of smooth fiber bundles over the circle with a common $4$-dimensional fiber with the following properties: (1) their total spaces are diffeomorphic to each other; (2) they are isomorphic to each other as topological fiber…

In this paper we show that even in the case of simply connected minimal algebraic surfaces of general type, deformation and differentiable equivalence do not coincide. Exhibiting several simple families of surfaces which are not deformation…

We describe a procedure to construct infinite sets of pairwise smoothly inequivalent 2-spheres in simply connected 4-manifolds, which are topologically isotopic and whose complement has a prescribed fundamental group that satisfies some…

We show examples of pairs of smooth, compact, homeomorphic 4-manifolds, whose diffeomorphism types are distinguished by the topology of the singular sets of smooth stable maps defined on them. In this distinction we rely on results from…

The Nielsen-Thurston theory of surface diffeomorphisms shows that useful dynamical information can be obtained about a surface diffeomorphism from a finite collection of periodic orbits.In this paper, we extend these results to homoclinic…

This is an expository paper giving a proof of the existence and uniqueness of smooth structures (hence also PL structures) on topological surfaces. Most published proofs rely on the topological Schoenflies theorem, but here we use instead…

In a closed 2-cell embedding of a graph each face is homeomorphic to an open disk and is bounded by a cycle in the graph. The Orientable Strong Embedding Conjecture says that every 2-connected graph has a closed 2-cell embedding in some…

M. A. Kervaire showed that every group of deficiency $d$ and weight $d$ is the fundamental group of a smooth sphere-link of $d$ components in a smooth homotopy 4-sphere. In the use of the smooth unknotting conjecture and the smooth 4D…

We show that the number of double points of smoothly immersed 2-spheres representing certain homology classes of an oriented, smooth, closed, simply-connected 4-manifold X must increase with the complexity of corresponding h-cobordisms from…

For each nonnegative integer m we show that any closed, oriented topological four-manifold with fundamental group Z_{4m+2} and odd intersection form, with possibly seven exceptions, either admits no smooth structure or admits infinitely…

A smooth ruled surface in 4-space has only parabolic points or inflection points of real type. We show, by means of contact with transverse planes, that at a parabolic point, there exist two tangent directions determining two planes along…

A celebrated theorem in two-dimensional dynamics due to John Franks asserts that every area preserving homeomorphism of the sphere has either two or infinitely many periodic points. In this work we reprove Franks' theorem under the…

A cyclic cover over the Riemann sphere branched at four points inherits a natural flat structure from the "pillow" flat structure on the basic sphere. We give an explicit formula for all individual Lyapunov exponents of the Hodge bundle…