Redbud Topology Seminar

The Redbud Topology Conference is a regional conference in topology and related areas, with participants from the University of Arkansas, the University of Oklahoma, Oklahoma State University, and elsewhere. Due to the ongoing coronavirus pandemic, we will continue to hold a virtual seminar during Spring 2022 in lieu of a traditional conference. The seminar will meet Wednesdays at 4 PM via Zoom.

Dates and Speakers:

• 2/23 Neil Hoffman, Oklahoma State University
• 3/30 Hung Tran, University of Oklahoma
• 4/13 Sumeyra Sakalli, University of Arkansas
• 4/27 Yan Mary He, University of Oklahoma

Register: A Zoom link will be sent to all registered participants. If you previously registered for the Fall seminar, there is no need to register again.

• REGISTER

Titles and Abstracts:

• Neil Hoffman, Oklahoma State University


• Title: Distinguishing Seifert fibered spaces and lens spaces
• Abstract: Lens spaces have finite cyclic fundamental groups. In this talk, I will discuss how to distinguish lens spaces from Seifert Fibered Spaces via proofs that generate certificates that are polynomially-sized relative to their triangulations. After giving an overview of this construction, I will discuss what is open in terms of distinguishing lens spaces from all 3-manifolds.


• ***


• Hung Tran, University of Oklahoma


• Title: Superexponential Dehn functions inside CAT(0) groups
• Abstract: We construct 4–dimensional CAT(0) groups containing finitely presented subgroups whose Dehn functions are exp⁽ⁿ⁾(x^m) for integers n, m ≥ 1 and 6–dimensional CAT(0) groups containing finitely presented subgroups whose Dehn functions are exp⁽ⁿ⁾(x^α) for integers n ≥ 1 and α dense in [1,∞). This significantly expands the known geometric behavior of subgroups of CAT(0) groups. This is a joint project with Noel Brady.


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• Sumeyra Sakalli, University of Arkansas


• Title: Complex ball quotients and new symplectic 4–manifolds with nonnegative signatures
• Abstract: We first construct a complex surface with positive signature, which is a ball quotient. We obtain it as an abelian Galois cover of ℂℙ² branched over the Hesse arrangement. Then we analyze its fibration structure, and by using it we build new symplectic and also non-symplectic exotic 4–manifolds with positive signatures.
  
  In the second part of the talk, we discuss Cartwright–Steger surfaces, which are also ball quotients. Next, we present our constructions of new symplectic and non-symplectic exotic 4–manifolds with non-negative signatures that have the smallest Euler characteristics in the so-called 'arctic region' on the geography chart.
  
  More precisely, we prove that there exist infinite families of irreducible symplectic and infinite families of irreducible non-symplectic, exotic 4–manifolds that have the smallest Euler characteristics among the all known simply connected 4–manifolds with nonnegative signatures and with more than one smooth structures. This is a joint work with A. Akhmedov and S.-K. Yeung.


• ***


• Yan Mary He, University of Oklahoma


• Title: The Nielsen realization problem for some big mapping class groups
• Abstract: In this talk, we will first see how surfaces of infinite type and their mapping class groups naturally arise in dynamics, especially in complex dynamics. Then we show that the mapping class group of the plane minus a Cantor set or the sphere minus a Cantor set cannot be realized as a subgroup of the homeomorphism group. This is joint work with Lei Chen.

Organizers: Matthew Clay*, Max Forester, Neil Hoffman, Yo'av Rieck*, Henry Segerman, Jing Tao.
(*local organizers)

Questions or comments? Please contact Matthew Clay.

Updated: Mon 18 Apr 2022 10:08:11 AM CDT