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3 results for “cleavage”

Higher Vector Bundlesmath.CT

Geometric models for representations up to homotopy using simplicial vector bundles.

problem Geometric models for representations up to homotopy of Lie groupoids.

method Application of higher analogs of cleavages in simplicial fibrations to geometric models.

result An equivalence between representations up to homotopy and simplicial vector bundles endowed with a cleavage.

higher Lie groupoids simplicial vector bundles representations up to homotopy cleavage Higher Grothendieck Correspondence

2021-09-02abs ↗pdf ↗

The Adjoint Representation of a Higher Lie Groupoidmath.CT

Extends adjoint representation concept to higher Lie groupoids.

problem Defining adjoint representation for higher Lie groupoids.

method Generalizes standard construction to higher Lie groupoids using simplicial vector bundles.

result Adjoint representation up to homotopy is well-defined and unique.

Lie groupoid adjoint representation higher Lie groupoid simplicial vector bundles representation up to homotopy

2023-12-22abs ↗pdf ↗

The Cleavage Operad and String Topology of Higher Dimensionmath.GT

For a manifold N embedded inside euclidean space R^{n+1}, we produce a coloured operad that acts on the space of maps from N to M, where M is a compact, oriented, smooth manifold. For N the unit sphere, we indicate how this gives homological actions, generalizing the action of the Cacti operad and retrieving the Chas-S…

2010-12-21abs ↗pdf ↗