Topological and Smooth Stacks
arXiv:math/0306176
Abstract
We review the basic definition of a stack and apply it to the topological and smooth settings. We then address two subtleties of the theory: the correct definition of a ``stack over a stack'' and the distinction between small stacks (which are algebraic objects) and large stacks (which are generalized spaces).
Cited by in corpus (42)
- Foundations of Topological Stacks I
- Lie Groupoids and Differentiable Stacks
- Non Abelian Differentiable Gerbes
- Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi-Yau 4-folds
- Undoing decomposition
- Hamiltonian group actions on symplectic Deligne-Mumford stacks and toric orbifolds
- Poisson geometry and Morita equivalence
- Differentiable Stacks and Gerbes
- Lie 2-algebras of vector fields
- Riemannian metrics on differentiable stacks
- On orientations for gauge-theoretic moduli spaces
- Orbispaces as differentiable stratified spaces
- General aspects of heterotic string compactifications on stacks and gerbes
- Four Equivalent Versions of Non-Abelian Gerbes
- Integrating Poisson manifolds via stacks
- D-manifolds, d-orbifolds and derived differential geometry: a detailed summary
- Stacky Hamiltonian actions and symplectic reduction
- Introduction to the Gopakumar-Vafa Large N Duality
- Parallel Transport on Principal Bundles over Stacks
- Enough vector bundles on orbispaces
- Orbifolds as stacks?
- A Framework for Geometric Field Theories and their Classification in Dimension One
- Categorical Equivalence and the Renormalization Group
- A new definition of Kuranishi space
- Moduli of Open Stable Maps to a Homogeneous Space
- Poisson manifolds and their associated stacks
- Strictification of etale stacky Lie groups
- Principal actions of stacky Lie groupoids
- Integrating central extensions of Lie algebras via Lie 2-groups
- Some new homology and cohomology theories of manifolds and orbifolds
- Lie II theorem for Lie algebroids via higher groupoids
- A groupoid approach to noncommutative T-duality
- Orbifold bordism and duality for finite orbispectra
- Sheaf Theory for Étale Geometric Stacks
- Orbifolds as diffeologies
- Orbifold Euler characteristics of non-orbifold groupoids
- Augmented Teichmuller Spaces and Orbifolds
- Inertia groups of a toric DM stack, fake weighted projective spaces, and labelled sheared simplices
- On symplectic vortex equations over a compact orbifold Riemann surface
- The lattice points of a stacky polytope
- A Differential Topological Model for Olfactory Learning and Representation
- On state sums, internalisation and unification