Geometric Monodromy and the Hyperbolic Disc

By I. Smith. 2000

58 citations recorded by the source corpus.

Symplectic four-manifolds give rise to Lefschetz fibrations, which are determined by monodromy representations of free groups in mapping class groups. We study the topology of Lefschetz fibrations by analysing the action of the monodromy on the universal cover of a smooth fibre. We give new and simple proofs that Lefschetz fibrations arising from pencils (i.e. with exceptional sections) never split as non-trivial fibre sums, and that no simple closed curve can be invariant to isotopy under the monodromy representation.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8f15edbd5c0601f20fad5224db1d55ccbd741529

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In Discrete Mathematics and Combinatorics

1. Burak Ozbagci
2. A. Stipsicz
3. D. Auroux
4. L. Katzarkov
5. I. Smith
6. Chris Wendl
7. John B. Etnyre
8. P. Lisca

In Geometry and Topology

1. L. Katzarkov
2. D. Auroux
3. I. Smith
4. Burak Ozbagci
5. A. Stipsicz
6. P. Seidel
7. M. Abouzaid
8. Yankı Lekili

In Mathematical Physics

1. D. Auroux
2. L. Katzarkov
3. I. Smith
4. A. Stipsicz
5. Burak Ozbagci
6. P. Seidel
7. M. Abouzaid
8. Yankı Lekili

Citations in the corpus

• Lefschetz pencils and divisors in moduli space (2000, methodology): “We recall a theorem of Stipsicz [26]; a simpler proof is given by the author in [21]:”
• Contact 3-manifolds with infinitely many Stein fillings (2003, background): “It is known (see [18]) that if for the relator w we have w = ∆g in Γ 1 g, then the Lefschetz fibration X → S(2) given by w admits a section of square −k.”
• Branched coverings of ℂℙ2 and invariants of symplectic 4-manifolds (2000, background): “It is also known that there does not exist any non-trivial element in the fundamental group of the generic fiber Σg which remains fixed by the monodromy of the Lefschetz fibration ([12], [11]).”