Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.35435

Orbifold Mapping Spaces via Bibundles

Yoshihiro Sugimoto
View original source ↗Read source document ↗Export metadata ↓

Abstract

The existence of orbifold structures on mapping spaces between orbifolds was established in previous work, notably by W. Chen and B. Chen-Du-Liao. In this paper, we construct an infinite-dimensional orbifold structure on the mapping space in a more geometric way, using bibundles (or Hilsum-Skandalis morphisms), based on Lerman's description of orbifold morphisms. We construct a proper étale (or Fréchet) Lie groupoid representing the mapping space in the $C^k$, $C^\infty$, and $W^{k,p}$ settings, and show that its Morita equivalence class is independent of the choices of groupoid presentations. Locally, the mapping groupoid is isomorphic to the action groupoid of a finite group, where the finite group is identified with the automorphism group of the corresponding bibundle. This provides a concrete geometric framework for further studies of mapping spaces and moduli spaces on orbifolds, with applications to Floer theory on symplectic orbifolds.

Explore related subjects

math.SGmath.DG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Yoshihiro Sugimoto. 2026-09-28. Orbifold Mapping Spaces via Bibundles. https://arxiv.org/abs/2609.35435

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Weighted Seshadri constants and ellipsoid embeddings

We explore Seshadri constants associated to weighted blow-ups of complex projective varieties and demonstrate how to use this notion to construct symplectic embeddings of ellipsoids. We illustrate the utility of this point of view by providing constructions of full fillings of $\mathbb{CP}^2$ by ellipsoids corresponding to all of the exceptional (post-Fibonacci) steps of the McDuff--Schlenk staircase and some non-obvious embeddings of ellipsoids in ellipsoids.

math.SG↗
arXiv2026

Kodaira fibres and wrapped Floer cohomology

Let $F$ be a singular fibre of a relatively minimal complex elliptic fibration with smooth total space, and let $Ω$ be a nonvanishing holomorphic two-form near $F$. We show that a small neighbourhood of $F$ is a Weinstein domain for $\mathrm{Re}\,Ω$ whose completion is a Legendrian surgery, with cocores obtained by completing holomorphic disks transverse to the components of $F$. For every coefficient field and every multiplicative bulk class, we compute the wrapped Floer cohomology of these cocores and prove that it is concentrated in degree zero. The cocores generate, so the bulk-deformed wrapped Fukaya category is equivalent to the category of perfect modules over an explicit algebra: a multiplicative preprojective algebra of affine type for the normal crossing fibres, and a quiver algebra with relations for types $II$, $III$ and $IV$. Applications include formality of the affine plumbing dg algebras, mirror equivalences with resolved affine surfaces at the trivial bulk class, and with quotient stacks of algebraic tori at root-of-unity bulk classes for the four star-shaped fibres.

math.SG↗
arXiv2026

Real Inertia, Phase Obstructions, and de Rham Algebras for Orientifolds

In this paper, we study de Rham realizations for finite orientifold quotients. On the orientation preserving inertia of an almost complex global quotient we construct an anti-linear involution of the Chen-Hu algebra whose fixed subalgebra is a real form of the Chen-Ruan algebra. For genuine orientation reversing fixed sectors we prove that no coordinate invariant single sector fractional age exists. When a Calabi-Yau volume line is preserved, the relative phases define a canonical class $[μ_{\mathbb R}]\in H^2(\widehat G;\mathbb Z_ε)$. We identify this class with the Bockstein obstruction to a coherent real phase lift and prove that its vanishing is equivalent, after rephasing the volume form, to a phase trivial orientifold action. We then formulate a general Euler-Gysin realization theorem using relative Fredholm bundles and determinant-line sewing. For phase trivial Calabi-Yau surfaces we verify the admissibility conditions directly and obtain a canonically defined associative graded cohomology algebra containing the Chen-Hu even sector and the odd fixed surfaces. For an Eisenstein abelian surface with an order six dihedral action we compute the centralizer invariant algebra explicitly; it is a $16$ dimensional Frobenius algebra whose odd sector multiplication is noncommutative in the shifted grading. We also explain the relation with earlier unoriented orbifold cohomology constructions.

math.SG↗