30 research outputs found
Commutators, Lefschetz fibrations and the signatures of surface bundles
We construct examples of Lefschetz fibrations with prescribed singular
fibers. By taking differences of pairs of such fibrations with the same
singular fibers, we obtain new examples of surface bundles over surfaces with
non-zero signature. From these we derive new upper bounds for the minimal genus
of a surface representing a given element in the second homology of a mapping
class group.Comment: 20 pages, 7 figures, accepted for publication in Topolog
Contact structures on M × S2 {Mathematical expression}
We show that if a manifold {Mathematical expression} admits a contact structure, then so does {Mathematical expression}. Our proof relies on surgery theory, a theorem of Eliashberg on contact surgery and a theorem of Bourgeois showing that if {Mathematical expression} admits a contact structure then so does {Mathematical expression}. © 2013 Springer-Verlag Berlin Heidelberg
Exotic smooth structures on 4-manifolds with zero signature
For every integer , we construct infinite families of mutually
nondiffeomorphic irreducible smooth structures on the topological -manifolds
and (2k-1)(\CP#\CPb), the connected sums of
copies of and \CP#\CPb.Comment: 6 page
A simply connected surface of general type with p_g=0 and K^2=2
In this paper we construct a simply connected, minimal, complex surface of
general type with p_g=0 and K^2=2 using a rational blow-down surgery and
Q-Gorenstein smoothing theory.Comment: 19 pages, 6 figures. To appear in Inventiones Mathematica
On a minimal factorization conjecture
Let be a proper holomorphic map from a connected complex surface S onto the open unit disk D⊂C, with 0∈D as its unique singular value, and having fiber genus g>0 -- Assume that in case g⩾2, admits a deformation whose singular fibers are all of simple Lefschetz type -- It has been conjectured that the factorization of the monodromy f∈M around ϕ (0) in terms of righ-thanded Dehn twists induced by the monodromy of has the least number of factors among all possible factorizations of f as a product of righthanded Dehn twists in the mapping class group (see [M. Ishizaka, One parameter families of Riemann surfaces and presentations of elements of mapping class group by Dehn twists, J. Math. Soc. Japan 58 (2) (2006) 585–594]) -- In this article, the validity of this conjecture is established for g=
Ozsvath-Szabo invariants and tight contact three-manifolds, II
Let p and n be positive integers with p>1, and let E(p,n) be the oriented 3-manifold obtained by performing pn(p-1)-1 surgery on a positive torus knot of type (p, pn+1). We prove that E(2,n) does not carry tight contact structures for any n, while E(p,n) carries tight contact structures for any n and any odd p. In particular, we exhibit the first infinite family of closed, oriented, irreducible 3-manifolds which do not support tight contact structures. We obtain the nonexistence results via standard methods of contact topology, and the existence results by using a quite delicate computation of contact Ozsvath-Szabo invariants
Contact Ozsváth–Szabó invariants and Giroux torsion
In this paper we prove a vanishing theorem for the contact Ozsvath--Szabo invariants of certain contact 3--manifolds having positive Giroux torsion. We use this result to establish similar vanishing results for contact structures with underlying 3--manifolds admitting either a torus fibration over the circle or a Seifert fibration over an orientable base. We also show -- using standard techniques from contact topology -- that if a contact 3--manifold (Y,\xi) has positive Giroux torsion then there exists a Stein cobordism from (Y,\xi) to a contact 3--manifold (Y,\xi') such that (Y,\xi) is obtained from (Y,\xi') by a Lutz modification
On the existence of tight contact structures on Seifert fibered 3-manifolds
We determine the closed, oriented Seifert fibered 3-manifolds which carry positive tight contact structures. Our main tool is a new non-vanishing criterion for the contact Ozsvath-Szabo invariant