Research

 

My research interests are in low-dimensional topology. I study 3 and 4 dimensional manifolds and knots in the 3-sphere. I tackle problems chiefly using Heegaard Floer homology tools, but I have also relied on Witt classes, Dedekind sums, Goeritz matrices, and others. Two tori

 


Publications and preprints

  1. Stanislav Jabuka, "Heegaard Floer groups of Dehn surgeries", ArXiv:1409.6236 (2014). To appear in the Journal of the London Mathematical Society.

  2. Stanislav Jabuka and Swatee Naik, "Self-diffeomorphisms of three-manifolds and Heegaard Floer homology" (2014). Unpublished notes on how a self-diffeomorphism of a three-manifold acts on its Heegaard Floer homology groups.

  3. Stanislav Jabuka and Swatee Naik, "Periodic knots and Heegaard Floer correction terms",ArXiv:1307.5116 (2013). To appear in the Journal of the European Mathematical Society.

  4. Stanislav Jabuka, "The signature of an even symmetric form with vanishing associated linking form", ArXiv:1204.4965 (2012).

  5. Stanislav Jabuka,"Heegaard Floer genus bounds for Dehn surgeries on knots", (2012), ArXiv.1202.4412. Published in the Journal of Topology.

  6. Stanislav Jabuka, Sinai Robins and Xinli Wang,"Heegaard Floer correction terms and Dedekind-Rademacher sums", ArXiv:1105.4397(2011). Published in the International Mathematics Research Notices.

  7. Stanislav Jabuka, Sinai Robins and Xinli Wang,"When are two Dedekind sums equal?", ArXiv:1103.0370 (2011). Published in the International Journal of Number Theory.

  8. Michael Gallaspy and Stanislav Jabuka, "The Goeritz matrix and signature of a two birdge knot", ArXiv:0910.2872 (2009). To appear in the Rocky Mountain Journal of Mathematics.

  9. Stanislav Jabuka, "The rational Witt class and the unknotting number of a knot", ArXiv:0907.2275 (2009).

  10. Stanislav Jabuka, "Concordance invariants from higher order covers", ArXiv:0908.1088 (2009). Published in Topology and its applications.

  11. Stanislav Jabuka, "Rational Witt classes of pretzel knots", ArXiv:0806.3245 (2008). Published in the Osaka Journal of Mathematics.

  12. Joshua Greene and Stanislav Jabuka, "The Slice-Ribbon Conjecture for 3-stranded pretzel knots", ArXiv:0706.3398 (2007). Published in the American Journal of Mathematics.

  13. Stanislav Jabuka and Thomas Mark, "Product formulae for Ozsvath-Szabo 4-manifold invariants", ArXiv:0706.0339 (2007). Published in Geometry and Topology.

  14. Stanislav Jabuka, "Heegaard Floer homology and knot concordance: a survery of recent advances" (2007). Published in Glasnik Matematicki Series III.

  15. Stanislav Jabuka and Swatee Naik, "Order in the concordance group and Heegaard Floer homology", ArXiv:0611023 (2006). Published in Geometry and Topology.

  16. Stanislav Jabuka and Thomas Mark, "On the Heegaard Floer homology of a surface times a circle", ArXiv:0502328 (2005). Published in Advances in Mathematics.

  17. Stanislav Jabuka and Thomas Mark, "Heegaard Floer homology of mapping tori. II", ArXiv:0410005 (2004). Published in "Geometry and topology of manifolds", 119–135, Fields Inst. Commun., 47, Amer. Math. Soc., Providence, RI, 2005.

  18. Stanislav Jabuka and Thomas Mark, "Heegaard Floer homology of certain mapping tori", ArXiv:0405314 (2004). Published in Algebraic and Geometric Topology.

  19. Stanislav Jabuka, "Symplectic surfaces and generic J-holomorphic structures on 4-manifolds", ArXiv:0207052 (2002). Published in the Illinois Journal of Mathematics.

  20. Stanislav Jabuka, "Dolbeaultova kohomologija na simplekticnim mnogostrukostima" (2003). Proceedings of the conference held in Ljubljana in June 2003 to mark the 30-th anniversary of the joint topological seminar Zagreb-Ljubljana (in Croatian).

  21. Stanislav Jabuka, "Grafting Seiberg-Witten monopoles", ArXiv:0110285 (2001). Published in Algebraic and Geometric Topology.

 

Office: 318 Davidson Mathematics and Science Center
Email: jabuka@unr.edu
Telephone: (775) 784-6816