7 papers
The surface category and tropical curves
Jan Steinebrunner
We compute the classifying space of the surface category whose objects are closed oriented -manifolds and whose morphisms are diffeomorphism classes of orient…
The prime decomposition fibre sequence for moduli spaces of reducible 3-manifolds
Rachael Boyd, Corey Bregman, Jan Steinebrunner
We study the moduli space , for a reducible, oriented 3-manifold with irreducible prime factors . A programme of César de Sá-Rourke, Hend…
The equifibered approach to -properads
Shaul Barkan, Jan Steinebrunner
We define a notion of -properads that generalises -operads by allowing operations with multiple outputs. Specializing to the case where each operation has a single…
Open 2D TFTs admit initial open-closed extensions
Shaul Barkan, Jan Steinebrunner, Adela YiYu Zhang
We show that any open 2-dimensional topological field theory valued in a symmetric monoidal -category (with suitable colimits) extends canonically to an open-closed field t…
2-dimensional TFTs via modular -operads
Jan Steinebrunner
This lecture series is based on joint work in progress with Shaul Barkan, as well as work in progress of the author. The five sections of these notes correspond to the five lecture…
Segalification and the Boardman-Vogt tensor product
Shaul Barkan, Jan Steinebrunner
We develop an analog of Dugger and Spivak's necklace formula providing an explicit description of the Segal space generated by an arbitrary simplicial space. We apply this to obtai…