163 citations · 426 across the 9 of their papers we have counts for
12 papers
Semisimple Field Theories Detect Stable Diffeomorphism
David Reutter, Christopher Schommer-Pries
Extending the work of the first author, we introduce a notion of semisimple topological field theory in arbitrary even dimension and show that such field theories necessarily lead…
Invertible Topological Field Theories
Christopher Schommer-Pries
A -dimensional invertible topological field theory is a functor from the symmetric monoidal -category of -bordisms (embedded into and equipped…
Tori Detect Invertibility of Topological Field Theories
Christopher Schommer-Pries
A once-extended d-dimensional topological field theory Z is a symmetric monoidal functor (taking values in a chosen target symmetric monoidal (infty,2)-category) assigning values t…
Modular categories as representations of the 3-dimensional bordism 2-category
Bruce Bartlett, Christopher L. Douglas, Christopher J. Schommer-Pries +1
We show that once-extended anomalous 3-dimensional topological quantum field theories valued in the 2-category of k-linear categories are in canonical bijection with modular tensor…
Extended 3-dimensional bordism as the theory of modular objects
Bruce Bartlett, Christopher L. Douglas, Christopher J. Schommer-Pries +1
A modular object in a symmetric monoidal bicategory is a Frobenius algebra object whose product and coproduct are biadjoint, equipped with a braided structure and a compatible twis…
The balanced tensor product of module categories
Christopher L. Douglas, Christopher Schommer-Pries, Noah Snyder
The balanced tensor product M (x)_A N of two modules over an algebra A is the vector space corepresenting A-balanced bilinear maps out of the product M x N. The balanced tensor pro…
Singular cohomology from supersymmetric field theories
Christopher Schommer-Pries, Nathaniel Stapleton
We show that Sullivan's model of rational differential forms on a simplicial set may be interpreted as a (kind of) -dimensional supersymmetric quantum field theory over $X…
Dualizable tensor categories
Christopher L. Douglas, Christopher Schommer-Pries, Noah Snyder
We investigate the relationship between the algebra of tensor categories and the topology of framed 3-manifolds. On the one hand, tensor categories with certain algebraic propertie…
Dualizability in Low-Dimensional Higher Category Theory
Christopher Schommer-Pries
These lecture notes form an expanded account of a course given at the Summer School on Topology and Field Theories held at the Center for Mathematics at the University of Notre Dam…
The Classification of Two-Dimensional Extended Topological Field Theories
Christopher J. Schommer-Pries
We provide a complete generators and relations presentation of the 2-dimensional extended unoriented and oriented bordism bicategories as symmetric monoidal bicategories. Thereby w…
On the Unicity of the Homotopy Theory of Higher Categories
Clark Barwick, Christopher Schommer-Pries
We axiomatise the theory of -categories. We prove that the space of theories of -categories is a . We prove that Rezk's complete Segal $Θ…
Central Extensions of Smooth 2-Groups and a Finite-Dimensional String 2-Group
Christopher Schommer-Pries
We provide a model of the String group as a central extension of finite-dimensional 2-groups in the bicategory of Lie groupoids, left-principal bibundles, and bibundle maps. This b…