About

R. İnanç Baykur is a professor in the Department of Mathematics and Statistics at the University of Massachusetts. He is based in the Lederle Graduate Research Tower in Amherst, MA. His contact information includes a phone number, fax, and email address, indicating his active engagement in academic and research activities. The webpage references his involvement in research, teaching, books, and professional links, suggesting a broad scope of academic contributions. However, specific details about his research focus, background, or key contributions are not provided in the available text.

Research topics

• Pure mathematics
• Mathematics
• Physics
• Combinatorics
• Geometry

Selected publications

• On four-manifolds without 1- and 3-handles

  arXiv (Cornell University) · 2024-03-21

  preprintOpen access1st authorCorresponding

  We note that infinitely many irreducible, closed, simply connected 4-manifolds, with prescribed signature and spin type, admit perfect Morse functions, i.e. they can be given handle decompositions without 1- and 3-handles. In particular, there are many such 4-manifolds homeomorphic but not diffeomorphic to the standard 4-manifolds # m (S^2 x S^2) and # n (CP^2 # -CP^2), respectively, which answers Problem 4.91 on Kirby's 1997 list.

  PublisherOA PDFDOI

• Stein fillings vs. Milnor fibers

  arXiv (Cornell University) · 2024-03-18

  preprintOpen access1st authorCorresponding

  Given a link of a normal surface singularity with its canonical contact structure, we compare the collection of its Stein fillings to its Milnor fillings (that is, Milnor fibers of possible smoothings). We prove that, unlike Stein fillings, Milnor fillings of a given link have bounded topology; for links of sandwiched singularities, we further establish that there are only finitely many Milnor fillings. We discuss some other obstructions for a Stein filling to be represented by a Milnor fiber, and for various types of singularities, including simple classes like cusps and triangle singularities, we produce Stein fillings that do not come from Milnor fibers or resolutions.

  PublisherOA PDFDOI

• Correction: Geography of surface bundles over surfaces

  Mathematische Annalen · 2024-06-12

  articleOpen access1st authorCorresponding
  PublisherOA PDFDOI

• Smooth structures on four-manifolds with finite cyclic fundamental groups

  arXiv (Cornell University) · 2024-06-13

  preprintOpen access1st authorCorresponding

  For each nonnegative integer m we show that any closed, oriented topological four-manifold with fundamental group Z_{4m+2} and odd intersection form, with possibly seven exceptions, either admits no smooth structure or admits infinitely many distinct smooth structures up to diffeomorphism. Moreover, we construct infinite families of non-complex irreducible fake projective planes with diverse fundamental groups.

  PublisherOA PDFDOI

• Nielsen realization in dimension four and projective twists

  arXiv (Cornell University) · 2023-04-20

  preprintOpen accessSenior author

  We demonstrate the existence of numerous non-spin 4-manifolds for which the smooth Nielsen realization problem fails; namely, there exist finite subgroups of their mapping class groups that cannot be realized by any group of diffeomorphisms. This extends and complements recent results for spin 4-manifolds. Our examples span virtually all possible intersection forms, both even and odd, indefinite and definite, and include many irreducible 4-manifolds. To derive these examples, we study multi-twists, projective twists, and multi-reflections, which are all mapping classes supported around collections of embedded spheres and projective planes. Our obstructions to Nielsen realization are based on the work of Konno. We investigate projective twists in further detail, and notably, employ them to show that, for many closed symplectic 4-manifolds, the symplectic Torelli group is not generated by squared Dehn twists.

  PublisherOA PDFDOI

• Spin Lefschetz fibrations are abundant

  arXiv (Cornell University) · 2023-03-03

  preprintOpen accessSenior author

  We prove that any finitely presented group can be realized as the fundamental group of a spin Lefschetz fibration over the 2-sphere. We moreover show that any admissible lattice point in the symplectic geography plane below the Noether line can be realized by a simply-connected spin Lefschetz fibration.

  PublisherOA PDFDOI

• Exotic 4-manifolds with signature zero

  arXiv (Cornell University) · 2023-05-18

  preprintOpen access1st authorCorresponding

  We produce infinitely many distinct irreducible smooth 4-manifolds homeomorphic to #(2m+1)(CP^2 # -CP^2) and #(2n+1)(S^2 x S^2), respectively, for each m>3 and n>4. These provide the smallest exotic closed simply connected 4-manifolds with signature zero known to date, and in each one of these homeomorphism classes, we get minimal symplectic 4-manifolds. Our novel exotic 4-manifolds are derived from fairly special small Lefschetz fibrations we build via positive factorizations in the mapping class group, with spin and non-spin monodromies.

  PublisherOA PDFDOI

• Geography of surface bundles over surfaces

  arXiv (Cornell University) · 2023-02-13

  preprintOpen access1st authorCorresponding

  We construct symplectic surface bundles over surfaces with positive signatures for all but 18 possible pairs of fiber and base genera. Meanwhile, we determine the commutator lengths of a few new mapping classes.

  PublisherOA PDFDOI

• Lefschetz fibrations with arbitrary signature

  Journal of the European Mathematical Society · 2023 · 6 citations

  1st authorCorresponding
  • Mathematics
  • Pure mathematics
  • Combinatorics

  We develop techniques to construct explicit symplectic Lefschetz fibrations over the 2 -sphere with any prescribed signature \sigma and any spin type when \sigma is divisible by 16 . This solves a long-standing conjecture on the existence of such fibrations with positive signature. As applications, we produce symplectic 4 -manifolds that are homeomorphic but not diffeomorphic to connected sums of S^2 \times S^2 , with the smallest topology known to date, as well as larger examples as symplectic Lefschetz fibrations.

  PublisherOA PDFDOI

• Unchaining surgery and topology of symplectic 4-manifolds

  Mathematische Zeitschrift · 2023 · 6 citations

  1st authorCorresponding
  • Mathematics
  • Pure mathematics
  • Physics
  PublisherDOI

Recent grants

• Topology of smooth and symplectic 4-manifolds

  NSF · $179k · 2015–2019

• Geometry and topology of 4-manifolds

  NSF · $284k · 2020–2024

• Geometry and topology of smooth four-manifolds

  NSF · $122k · 2009–2013

Frequent coauthors

• Jeremy Van Horn-Morris

  11 shared

• Kenta Hayano

  7 shared

• Osamu Saeki

  6 shared

• Naoyuki Monden

  Okayama University of Science

  5 shared

• Stefan Friedl

  University of Regensburg

  5 shared

• Mustafa Korkmaz

  Middle East Technical University

  5 shared

• Mustafa Korkmaz

  Middle East Technical University

  5 shared

• Dan Margalit

  4 shared