Group actions on smooth 4-manifolds

October 25-26, 2013, University of Massachusetts, Amherst, MA

Organizing Committee

R. Inanc Baykur (University of Massachusetts), Weimin Chen (University of Massachusetts) and Daniel Ruberman (Brandeis University)

Speakers and participants

  • Anar Akhmedov (University of Minnesota)
  • Nima Anvari (Max Planck Institute, Bonn)
  • Richard Buckman (University of Massachusetts, Amherst)
  • Alan Durfee (Mount Holyoke College)
  • Ian Hambleton (McMaster University)
  • Andrew Havens (University of Massachusetts, Amherst)
  • Daniel Herr (Wheaton College)
  • Tynan Kelly (Brandeis University)
  • Tian-Jun Li (University of Minnesota)
  • Devin Murray (Brandeis University)
  • Katherine Raoux (Brandeis University)
  • Nikolai Saveliev (University of Miami)
  • Michael Sullivan (University of Massachusetts, Amherst)
  • Nathan Sunukjian (Max Planck Institute / Stony Brook)
  • Biji Wong (Brandeis University)
  • Weiwei Wu (Michigan State University)


The aim of this 2-day workshop is to bring together active researchers in group actions and smooth 4-manifolds, ranging from leading experts to recent PhDs and graduate students, and provide a panorama of the field through a variety of talks and discussion sessions.

Registration and support

No registration is needed; if you are planning on attending the workshop, simply e-mail any one of the organizers to let us know about it. We have reserved rooms for all the invited participants outside of Western Massachusetts at the UMass Hotel and Conference Center. This event is sponsored by University of Massachusetts funds (R. Inanc Baykur) and by the NSF FRG Grant DMS 1065784 and 1065827 as a part of the FRG Collaborative Research on "Topology and Invariants of Smooth 4-Manifolds" (Weimin Chen and Daniel Ruberman).


Friday, October 25

  9:15-10:15am Tian-Jun Li
10:45-11:45am Ian Hambleton
11:45-12:15pm Discussion
12:15- 2:00pm  Lunch
  2:00- 3:00pm Nathan Sunukjian
  3:30- 4:30pm Weiwei Wu
  4:30- 5:00pm  Tea
  5:00- 6:00pm  Discussion
Saturday, October 26

  9:15-10:15am Nima Anvari
10:45-11:45am Daniel Herr
11:45- 1:15pm  Discussion
  1:15- 3:15pm  Lunch

All talks will be held at Room 1634 Lederle Graduate Research Tower, University of Massachusetts, Amherst. Friday group lunch will be at the University Club and tea will be at the lounge next to Room 1634. Directions to University of Massachusetts campus can be found here. Department of Mathematics and Statistics is located in the Lederle Graduate Research Tower (LGRT) which is a very short walking distance from the UMass Hotel. (UMass Campus map -pdf)

Titles and abstracts of talks

  • Nima Anvari
    Equivariant splitting of 4-Manifolds
    In this talk we consider free finite cyclic group actions on Seifert fibered homology spheres extending to smooth, homologically trivial actions on bounding, even negative definite 4-manifolds. We obtain restrictions using equivariant Yang-Mills gauge theory and as an application study smooth equivariant splittings of 4-manifolds.

  • Ian Hambleton
    Smooth group actions on S^2 x S^2 and Yang-Mills gauge theory
    In the talk I will describe how certain constraints on smooth finite group actions on 4-manifolds arise from studying an equivariant version of the Yang-Mills moduli spaces. The main application is the conjecture that smooth actions of cyclic groups on S^2 x S^2 have standard rotation numbers.

  • Daniel Herr
    Open books on contact orbifolds
    On 3-manifolds, every open book supports a contact structure, and every contact structure is supported by an open book. This correspondence is due to Giroux, and is a major tool in the study of three dimensional contact geometry. I will discuss the extension of this result to the equivariant and orbifold categories.

  • Tian-Jun Li
    Geometric automorphism group of symplectic 4-manifolds
    I will present some results about the homological action of the orientation-preserving diffeomorphism group of a symplectic 4-manifold. (Joint work with Bo Dai and Chung-I Ho).

  • Nathan Sunukjian
    Embedded surfaces and exotic group actions
    It has long been known that exotic smooth structures on a 4-manifold become the same after connect summing with enough copies of S^2 x S^2. There are two other notable kinds of exotic behavior observed in 4-manifolds: exotic embeddings of surfaces, and exotic group actions. In this talk I'll explain the interrelations between these different kinds of exotic behaviors, and I'll describe an operation under which such exotic things again become smoothly equivalent. This work in progress is joint with Inanc Baykur.

  • Weiwei Wu
    Finite subgroups of symplectic Cremona group
    Finite subgroup of Cremona group is a classical topic in algebraic geometry since the 19th century. In this talk we explain an extension of this problem to the symplectic category. In particular, we will explain the symplectic counterparts of two classical theorems. The first one due to Noether, says a plane Cremona map is decomposed into a sequence of quadratic transformations, which is generalized to the symplectic category on the homological level. The second one is due to Castelnuovo and Kantor, which says a minimal G-surface either has a conic bundle structure or is a Del Pezzo surface. The latter theorem lies the ground of classifications of finite Cremona subgroups due to Dolgachev and Iskovskikh. This is an ongoing program joint with Weimin Chen and Tian-Jun Li.