• Corpus ID: 240354772

The geometric cobordism hypothesis

  title={The geometric cobordism hypothesis},
  author={Daniel Grady and Dmitri Pavlov},
We prove a generalization of the cobordism hypothesis of Baez–Dolan and Hopkins–Lurie for bordisms with arbitrary geometric structures, such as Riemannian or Lorentzian metrics, complex and symplectic structures, smooth maps to a fixed target manifold, principal bundles with connections, or geometric string structures. Our methods rely on the locality property for fully extended functorial field theories established in arXiv:2011.01208, reducing the problem to the special case of geometrically… 

Figures from this paper

Integrals detecting degree 3 string cobordism classes

. The third string bordism group is known to be Z { 24 Z . Using Waldorf’s notion of a geometric string structure on a manifold, Bunke–Naumann and Redden have exhibited integral formulas involving

Functorial Statistical Physics: Feynman--Kac Formulae and Information Geometries

. The main results of this paper comprise proofs of the following two related facts: (i) the Feynman–Kac formula is a functor F ∗ , namely, between a stochastic dif-ferential equation and a dynamical

What bordism-theoretic anomaly cancellation can do for U

. We perform a bordism computation to show that the E 7(7) ( R ) U-duality symmetry of 4d N = 8 supergravity could have an anomaly invisible to perturbative methods; then we show that this anomaly is

Computads and string diagrams for $n$-sesquicategories

. An n -sesquicategory is an n -globular set with strictly associative and unital composition and whiskering operations, which are however not re-quired to satisfy the Godement interchange laws which

Snowmass White Paper: The Quest to Define QFT

This article provides a review of the literature on rigorous definitions and constructions in Quantum Field Theory, spanning the period of seven decades. Comparing with the ideas and constructions



Extended field theories are local and have classifying spaces

We show that all extended functorial field theories, both topological and nontopological, are local. We define the smooth (∞, d)-category of bordisms with geometric data, such as Riemannian metrics

A Framework for Geometric Field Theories and their Classification in Dimension One

A general framework of geometric functorial field theories is developed, meaning that all bordisms in question are endowed with geometric structures, so that it makes sense to require the output of the authors' field theory to depend smoothly on the input.

A quadratic refinement of the Grothendieck-Lefschetz-Verdier trace formula

We prove a trace formula in stable motivic homotopy theory over a general base scheme, equating the trace of an endomorphism of a smooth proper scheme with the "Euler characteristic integral" of a

A note on the (∞,n)–category of cobordisms

In this note we give a precise definition of fully extended topological field theories a la Lurie. Using complete n-fold Segal spaces as a model, we construct an $(\infty,n)$-category of

The Space of Framed Functions is Contractible

According to Igusa (Ann Math 119:1–58, 1984) a generalized Morse function on M is a smooth function \(M \rightarrow \mathbb{R}\) with only Morse and birth-death singularities and a framed function on

Fivebrane Structures

We study the cohomological physics of fivebranes in type II and heterotic string theory. We give an interpretation of the one-loop term in type IIA, which involves the first and second Pontrjagin

A Prehistory of n-Categorical Physics

This paper traces the growing role of categories and n-categories in physics, starting with groups and their role in relativity, and leading up to more sophisticated concepts which manifest

The cobordism category and Waldhausen's K-theory

This paper examines the category C^k_{d,n} whose morphisms are d-dimensional smooth manifolds that are properly embedded in the product of a k-dimensional cube with an (d+n-k)-dimensional Euclidean