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- Creator:
- Fuller, Terry
- Description:
- We show that there are homeomorphisms of closed oriented genus surfaces which are fiber-preserving with respect to an irregular branched covering and isotopic to the identity, but which are not fiber-isotopic to the identity.
- Resource Type:
- Article
- Identifier:
- 1088-6826, 0002-9939
- Campus Tesim:
- Northridge
- Creator:
- Etnyre, John B. and Fuller, Terry
- Description:
- We show that any 4-manifold, after surgery on a curve, admits an achiral Lefschetz fibration. In particular, if X is a simply connected 4-manifold we show that X#S 2 × S 2 and X#S 2×eS 2 both admit achiral Lefschetz fibrations. We also show these surgered manifolds admit near-symplectic structures and prove more generally that achiral Lefschetz fibrations with sections have near-symplectic structures. As a corollary to our proof we obtain an alternate proof of Gompf’s result on the existence of symplectic structures on Lefschetz pencils.
- Resource Type:
- Article
- Identifier:
- http://people.math.gatech.edu/~etnyre/preprints/papers/achiral.pdf, 1073-7928
- Campus Tesim:
- Northridge
- Creator:
- Fuller, Terry
- Description:
- Let M be a smooth 4-manifold which admits a relatively minimal hyperelliptic genus h Lefschetz fibration over S2. If all of the vanishing cycles for this fibration are nonseparating curves, then we show that M is a 2-fold cover of an S2-bundle over S2, branched over an embedded surface. If the collection of vanishing cycles for this fibration includes σ separating curves, we show that M is the relative minimalization of a Lefschetz fibration constructed as a 2-fold branched cover of ℂP2#(2σ + 1)ℂP2, branched over an embedded surface.
- Resource Type:
- Article
- Identifier:
- 0030-8730
- Campus Tesim:
- Northridge