Geometric Topology

Scope of the special session

Geometric topology, namely the use of geometric methods in low-dimensional topology, group theory and related subjects, has been one of the central themes of mathematics from the late 1970's, starting from the spectacular results and conjectures of Thurston. The crucial relevance of the topic is witnessed for instance by the large number of Fields medals awarded to mathematicians whose main research was carried out in geometric topology (Thurston, Freedman, Jones, Witten, Kontsevich, McMullen, Perelman). The concern that Perelman's proof of the (Poincaré and) geometrization conjecture(s) would weaken the activity in the field has proved groundless, and research is still developing at high speed, with the achievement of deep results (to mention just one, and a very recent one, Agol's final word on the proof of the virtual fibering conjecture) and the opening of intriguing new directions. Geometric methods are still proving very powerful in facing problems in low-dimensional topology and group theory, and they have applications to related fields, such as quantum topology and Teichmüller theory. The proposed special session wants to put emphasis on aspects of geometric topology that appear to be extremely lively and intertwined, such as hyperbolic three-manifolds, triangulations, growth and cohomology of groups. One of the leading themes will be the simplicial volume, a tool introduced by Gromov that reflects the link between geometry and topology for hyperbolic manifolds, and has been used by several of the proposed speakers.

Organisers

  • Carlo Petronio (University of Pisa, Italy) - petronio@dm.unipi.it
  • Joan Porti (Autonomous University of Barcelona, Spain)

Abstracts and schedule

Below you can download the schedule and the abstracts of all talks of this special session.

Speakers

  • Javier Aramayona (Paul Sabatier University, Toulouse, France)

          Homomorphisms from right-angled Artin groups to mapping class groups

  • Bruno Benedetti (Free University of Berlin, Germany)

           Embeddability of collapsible complexes

  • Michel Boileau (Aix-Marseille University, France)

           Hidden symmetries and commensurability of hyperbolic knot complements

  • Antonio Costa González (National Distance Education University, Spain)

           Doubles of Klein surfaces and 3-manifolds

  • Raquel Díaz Sánchez (Complutense University of Madrid, Spain)

           Schottky type uniformizations of stable Riemann orbifolds

  • Stefano Francaviglia (University of Bologna, Italy)

           Moduli spaces of branched projective structures

  • Roberto Frigerio (University of Pisa, Italy)

           Quasi-cocycles and bounded cohomology in higher degree

  • Ana García Lecuona (Aix-Marseille University, France)

           The colored signature of a splice link

  • Yuya Koda (Tohoku University, Japan)

           Stable maps and branched shadows of 3-manifolds

  • Bruno Martelli (University of Pisa, Italy)

           Some hyperbolic four-manifolds constructed using right-angled polytopes

  • Christoforos Neofytidis (University of Munich, Germany)

           The domination relation and branched covers

  • Cristina Pagliantini (ETH Zürich, Switzerland)

           The simplicial volume of 3-manifolds with boundary

  • Alessandro Sisto (ETH Zürich, Switzerland)

           On the bounded cohomology of acylindrically hyperbolic groups

  • Juan Souto (University of Rennes 1, France)

          Free vs. locally free Kleinian groups

  • Anastasiia Tsvietkova (Louisiana State University, USA)

           Hyperbolic volume and the coefficients of the colored Jones polynomial of alternating links

  • Shicheng Wang (Peking University, China)

           Embedding surfaces into S3 with maximum symmetry