On the space of super maps between smooth supermanifolds

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.