The G2T2 (Geometry, Group Theory, Topology) seminar is a seminar run (predominantly) by postdocs and students, with (predominantly) postdoc and student speakers. The organisers (in alphabetical order) consist of: Yifei CAI 蔡逸飞, Xiao CHEN 陈啸, Diptaishik CHOUDHURY, Qiliang LUO 罗琪亮, Tuo SUN 孙拓, Ivan TELPUKHOVSKIY, and Daxun WANG 王大洵 (*). 

Upcoming talks

Abdul ZALLOUM (Harbin Institute of Technology)

Hierarchical hyperbolicity from a cubical perspective

The theory of hierarchically hyperbolic spaces (HHSs) emerged from the observation that many cocompact CAT(0) cube complexes (CCCs) exhibit a structure analogous to that of mapping class groups and Teichmüller spaces. In particular, the powerful machinery of subsurface projections, which plays a fundamental role in the study of mapping class groups and Teichmüller spaces, extends to a broad class of CCCs. This insight not only led to the definition of HHSs but also raised the natural question of whether the reverse perspective holds: Can techniques from CCCs be leveraged to study mapping class groups, Teichmüller spaces, and HHSs more generally? In this talk, I will define these key objects and discuss recent developments that shed light on this question.

Time: 2025-03-28, Friday 10:00-11:30AM

Place: Ningzhai (宁斋) 203

Past talks

Yu HUANG 黄煜 (PKU)

Profinite rigidity and geometric topology of hyperbolic 3-manifolds

Profinite completion of fundamental groups of 3-manifolds encodes a lot of topological and geometrical information. Further more, it is interesting to ask whether the profinite completion can identify uniquely the homeomorphism type of a 3-manifold. Particularly, the hyperbolic manifold case is a long-term open question.

In fact, the profinitely rigid finite-volumn hyperbolic manifolds form a closed set under the geometric topology. From this observation, we produce plenty of examples of profinitely rigid cusped hyperbolic manifolds using bubble-drilled construction. The big rigid family includes Whitehead link complement and Borromean ring complement. If time permits, we will introduce how to handle the bubble-drilled construction manually.

Jumpei YASUDA (Osaka University / Osaka Metropolitan University)

2-bridge knots and 2-plat 2-knots

A 2-bridge knot is an embedded loop in the 3-sphere S^3 with at most two maximal points. For a rational number a/p, a 2-bridge knot K(a/p) is constructed based on this rational number. The double branched cover of S^3 along K(a/p) is diffeomorphic to the lens space L(a/p). Schubert classified 2-bridge knots by applying the classification of lens spaces.

A 2-knot is a (smoothly) embedded 2-sphere in the 4-sphere S^4. In this talk, we introduce a new class of 2-knots, called 2-plat 2-knots. We provide a normal form F(a/p) for 2-plat 2-knots and compute several invariants. Additionally, we propose questions concerning the classification of 2-plat 2-knots.

(*): Yi Huang also occasionally helps out a tiny bit.