Enough vector bundles on orbispaces

Abstract

We show that every orbispace satisfying certain mild hypotheses has 'enough' vector bundles. It follows that the K-theory of finite rank vector bundles on such orbispaces is a cohomology theory. Global presentation results for smooth orbifolds and derived smooth orbifolds also follow.

arXiv comment40 pages, to appear in Compositio Mathematica

References in corpus (7)

• Global homotopy theory
• Foundations of Topological Stacks I
• Topological and Smooth Stacks
• Twisted Orbifold K-Theory
• Gromov-Witten invariants of general symplectic manifolds
• Homotopy Theory of Orbispaces
• Orbispaces, orthogonal spaces, and the universal compact Lie group

Cited by in corpus (7)

• Orbifolds, Orbispaces and Global Homotopy Theory
• Orbifold bordism and duality for finite orbispectra
• Complex cobordism, Hamiltonian loops and global Kuranishi charts
• $\infty$-category and some applications on orbifolds
• Pseudolimits for Tangent Categories with Applications to Equivariant Algebraic and Differential Geometry
• The Mumford conjecture (after Bianchi)
• Free and based path groupoids