Geodesic
Universal Lefschetz fibrations over bounded surfaces
Zuddas, Daniele1
1Dipartimento di Matematica e Informatica, Università di Cagliari, Via Ospedale 72, 09124 Cagliari, Italy
Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1811-1829
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In 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.

DOI : 10.2140/agt.2012.12.1811
Classification : 55R55, 57N13
Keywords: universal Lefschetz fibration, Dehn twist, 4–manifold

Zuddas, Daniele  1

1 Dipartimento di Matematica e Informatica, Università di Cagliari, Via Ospedale 72, 09124 Cagliari, Italy 
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Zuddas, Daniele. Universal Lefschetz fibrations over bounded surfaces. Algebraic and Geometric Topology, Tome 12 (2012) no. 3, pp. 1811-1829. doi: 10.2140/agt.2012.12.1811

[1] N Apostolakis, R Piergallini, D Zuddas, Lefschetz fibrations over the disk

[2] J B Etnyre, T Fuller, Realizing 4–manifolds as achiral Lefschetz fibrations, Int. Math. Res. Not. 2006 (2006) 21

[3] R E Gompf, A I Stipsicz, 4–manifolds and Kirby calculus, Graduate Studies in Mathematics 20, American Mathematical Society (1999)

[4] A Gramain, Le type d'homotopie du groupe des difféomorphismes d'une surface compacte, Ann. Sci. École Norm. Sup. 6 (1973) 53

[5] J L Harer, Pencils of curves on 4–manifolds, PhD thesis, University of California, Berkeley (1979)

[6] W B R Lickorish, An introduction to knot theory, Graduate Texts in Mathematics 175, Springer (1997)

[7] A Loi, R Piergallini, Compact Stein surfaces with boundary as branched covers of $B^4$, Invent. Math. 143 (2001) 325

[8] J W Milnor, J D Stasheff, Characteristic classes, Annals of Mathematics Studies 76, Princeton Univ. Press (1974)

[9] A Phillips, Submersions of open manifolds, Topology 6 (1967) 171

[10] B Wajnryb, An elementary approach to the mapping class group of a surface, Geom. Topol. 3 (1999) 405

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