Lantern substitution and new symplectic 4-manifolds with b2 + = 3

Anar Akhmedov, Jun Yong Park

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Motivated by the construction of H. Endo and Y. Gurtas, changing a positive relator in Dehn twist generators of the mapping class group by using lantern substitutions, we show that 4-manifold K3#2CP2 equipped with the genus two Lefschetz fibration can be rationally blown down along six disjoint copies of the configuration C2. We compute the Seiberg-Witten invariants of the resulting symplectic 4-manifold, and show that it is symplectically minimal. Using our example, we also construct an infinite family of pairwise non-diffeomorphic irreducible symplectic and non-symplectic 4-manifolds homeomorphic to M = 3CP2#(19 - k)CP2 for 1 ≤ k ≤ 4.

Original languageEnglish (US)
Pages (from-to)1-17
Number of pages17
JournalMathematical Research Letters
Volume21
Issue number1
DOIs
StatePublished - 2014

Keywords

  • 4-manifold
  • Lantern relation
  • Lefschetz fibration
  • Mapping class group
  • Rational blowdown

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