Lefschetz Fibrations and real Lefschetz fibrations

Nermin Salepci[1]

  • [1] Institut Camille Jordan, Université Lyon I, 43, Boulevard du 11 Novembre 1918 69622 Villeurbanne Cedex, France

Winter Braids Lecture Notes (2014)

  • Volume: 1, page 1-19
  • ISSN: ?? -

Abstract

top
This note is based on the lectures that I have given during the winter school Winter Braids IV, School on algebraic and topological aspects of braid groups held in Dijon on 10 - 13 February 2014. The aim of series of three lectures was to give an overview of geometrical and topological properties of 4-dimensional Lefschetz fibrations. Meanwhile, I could briefly introduce real Lefschetz fibrations, fibrations which have certain symmetry, and could present some interesting features of them.This note will be yet another survey article on Lefschetz fibrations. There are excellent lecture notes/ survey papers/ book chapters on Lefschetz fibrations. You can, for example, look at [3], [11], [14], [20] among many others. In this note I intent to take my time on real Lefschetz fibrations as much as on Lefschetz fibrations in order not to repeat what was already done perfectly.

How to cite

top

Salepci, Nermin. "Lefschetz Fibrations and real Lefschetz fibrations." Winter Braids Lecture Notes 1 (2014): 1-19. <http://eudml.org/doc/275716>.

@article{Salepci2014,
abstract = {This note is based on the lectures that I have given during the winter school Winter Braids IV, School on algebraic and topological aspects of braid groups held in Dijon on 10 - 13 February 2014. The aim of series of three lectures was to give an overview of geometrical and topological properties of 4-dimensional Lefschetz fibrations. Meanwhile, I could briefly introduce real Lefschetz fibrations, fibrations which have certain symmetry, and could present some interesting features of them.This note will be yet another survey article on Lefschetz fibrations. There are excellent lecture notes/ survey papers/ book chapters on Lefschetz fibrations. You can, for example, look at [3], [11], [14], [20] among many others. In this note I intent to take my time on real Lefschetz fibrations as much as on Lefschetz fibrations in order not to repeat what was already done perfectly.},
affiliation = {Institut Camille Jordan, Université Lyon I, 43, Boulevard du 11 Novembre 1918 69622 Villeurbanne Cedex, France},
author = {Salepci, Nermin},
journal = {Winter Braids Lecture Notes},
language = {eng},
pages = {1-19},
publisher = {Winter Braids School},
title = {Lefschetz Fibrations and real Lefschetz fibrations},
url = {http://eudml.org/doc/275716},
volume = {1},
year = {2014},
}

TY - JOUR
AU - Salepci, Nermin
TI - Lefschetz Fibrations and real Lefschetz fibrations
JO - Winter Braids Lecture Notes
PY - 2014
PB - Winter Braids School
VL - 1
SP - 1
EP - 19
AB - This note is based on the lectures that I have given during the winter school Winter Braids IV, School on algebraic and topological aspects of braid groups held in Dijon on 10 - 13 February 2014. The aim of series of three lectures was to give an overview of geometrical and topological properties of 4-dimensional Lefschetz fibrations. Meanwhile, I could briefly introduce real Lefschetz fibrations, fibrations which have certain symmetry, and could present some interesting features of them.This note will be yet another survey article on Lefschetz fibrations. There are excellent lecture notes/ survey papers/ book chapters on Lefschetz fibrations. You can, for example, look at [3], [11], [14], [20] among many others. In this note I intent to take my time on real Lefschetz fibrations as much as on Lefschetz fibrations in order not to repeat what was already done perfectly.
LA - eng
UR - http://eudml.org/doc/275716
ER -

References

top
  1. E. Artin, Theory of braids, Ann. of Math. (2) 48 (1947), 101-126 Zbl0030.17703MR19087
  2. Denis Auroux, A stable classification of Lefschetz fibrations, Geom. Topol. 9 (2005), 203-217 (electronic) Zbl1084.57024MR2115673
  3. Denis Auroux, Fabrizio Catanese, Marco Manetti, Paul Seidel, Bernd Siebert, Ivan Smith, Gang Tian, Symplectic 4-manifolds and algebraic surfaces, 1938 (2008), Springer-Verlag, Berlin; Fondazione C.I.M.E., Florence MR2463711
  4. Ana Cannas da Silva, Lectures on symplectic geometry, 1764 (2001), Springer-Verlag, Berlin Zbl1016.53001MR1853077
  5. Kenneth Nicholas Chakiris, The monodromy of genus two pencils, (1983), ProQuest LLC, Ann Arbor, MI MR2633010
  6. Gaston Darboux, Sur le problème de Pfaff, Bull. Sci. Math. 6 (1882), 1-35 
  7. Alex Degtyarev, Nermin Salepci, Products of pairs of Dehn twists and maximal real Lefschetz fibrations, Nagoya Math. J. 210 (2013), 83-132 Zbl1304.14074MR3079276
  8. M. Dehn, Die Gruppe der Abbildungsklassen, Acta Math. 69 (1938), 135-206 Zbl0019.25301MR1555438
  9. S. K. Donaldson, Lefschetz pencils on symplectic manifolds, J. Differential Geom. 53 (1999), 205-236 Zbl1040.53094MR1802722
  10. Clifford J. Earle, James Eells, A fibre bundle description of Teichmüller theory, J. Differential Geometry 3 (1969), 19-43 Zbl0185.32901MR276999
  11. Terry Fuller, Lefschetz fibrations of 4-dimensional manifolds, Cubo Mat. Educ. 5 (2003), 275-294 Zbl1162.57303MR2065735
  12. Damien Gayet, Hypersurfaces symplectiques réelles et pinceaux de Lefschetz réels, J. Symplectic Geom. 6 (2008), 247-266 Zbl1170.53069MR2448826
  13. Robert E. Gompf, Toward a topological characterization of symplectic manifolds, J. Symplectic Geom. 2 (2004), 177-206 Zbl1084.53072MR2108373
  14. Robert E. Gompf, András I. Stipsicz, 4 -manifolds and Kirby calculus, 20 (1999), American Mathematical Society, Providence, RI Zbl0933.57020MR1707327
  15. A. Kas, On the handlebody decomposition associated to a Lefschetz fibration, Pacific J. Math. 89 (1980), 89-104 Zbl0457.14011MR596919
  16. Mustafa Korkmaz, Noncomplex smooth 4-manifolds with Lefschetz fibrations, Internat. Math. Res. Notices (2001), 115-128 Zbl0977.57020MR1810689
  17. Dusa McDuff, Dietmar Salamon, Introduction to symplectic topology, (1995), The Clarendon Press, Oxford University Press, New York Zbl0844.58029MR1373431
  18. Boris Moishezon, Complex surfaces and connected sums of complex projective planes, (1977), Springer-Verlag, Berlin-New York Zbl0392.32015MR491730
  19. Burak Ozbagci, András I. Stipsicz, Noncomplex smooth 4 -manifolds with genus- 2 Lefschetz fibrations, Proc. Amer. Math. Soc. 128 (2000), 3125-3128 Zbl0951.57015MR1670411
  20. Burak Ozbagci, András I. Stipsicz, Surgery on contact 3-manifolds and Stein surfaces, 13 (2004), Springer-Verlag, Berlin; János Bolyai Mathematical Society, Budapest Zbl1067.57024MR2114165
  21. Nermin Salepci, Real Lefschetz fibrations, (2007), Université Louis Pasteur. Institut de Recherche Mathématique Avancée (IRMA), Strasbourg Zbl1216.55004MR2780321
  22. Nermin Salepci, Real elements in the mapping class group of T 2 , Topology Appl. 157 (2010), 2580-2590 Zbl1213.57024MR2719402
  23. Nermin Salepci, Classification of totally real elliptic Lefschetz fibrations via necklace diagrams, J. Knot Theory Ramifications 21 (2012) Zbl1270.57063MR2926572
  24. Nermin Salepci, Invariants of totally real Lefschetz fibrations, Pacific J. Math. 256 (2012), 407-434 Zbl1282.57027MR2944983
  25. Bernd Siebert, Gang Tian, On hyperelliptic C ∞ -Lefschetz fibrations of four-manifolds, Commun. Contemp. Math. 1 (1999), 255-280 Zbl0948.57018MR1696101
  26. Bernd Siebert, Gang Tian, On the holomorphicity of genus two Lefschetz fibrations, Ann. of Math. (2) 161 (2005), 959-1020 Zbl1090.53072MR2153404
  27. Ivan Smith, Lefschetz fibrations and the Hodge bundle, Geom. Topol. 3 (1999), 211-233 (electronic) Zbl0929.53047MR1701812
  28. Ivan Smith, Symplectic Geometry of Lefschetz Fibrations, (1999), University of Oxford 
  29. N. E. Steenrod, The classification of sphere bundles, Ann. of Math. (2) 45 (1944), 294-311 Zbl0060.41412MR9857
  30. W. P. Thurston, Some simple examples of symplectic manifolds, Proc. Amer. Math. Soc. 55 (1976), 467-468 Zbl0324.53031MR402764

NotesEmbed ?

top

You must be logged in to post comments.