On the space of super maps between smooth supermanifolds
G.Bonavolont\`a, A.Kotov

TL;DR
This paper offers a geometric framework for understanding the space of super maps between smooth supermanifolds using infinite-dimensional super-vector bundles, moving beyond traditional functorial approaches.
Contribution
It introduces a novel geometric description of supermanifold mapping spaces via infinite-dimensional super-vector bundles, expanding the theoretical understanding.
Findings
Provides a geometric model for supermanifold mapping spaces
Connects functorial and geometric perspectives
Lays groundwork for further geometric analysis of supermaps
Abstract
Mapping spaces of supermanifolds are usually thought as exclusively in functorial terms (i.e. trough the Grothendieck functor of points). In this work we provide a geometric description of such mapping spaces in terms of infinite-dimensional super-vector bundles.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Geometry and complex manifolds
