Products of manifolds with fibered corners

TL;DR

This paper introduces a new category of manifolds with fibered corners, generalizing existing resolutions of stratified spaces and many body products, with a natural product called the 'ordered product' that supports specific geometric metrics.

Contribution

It defines a category of fibered corners manifolds with products and transverse fiber products, extending previous resolutions and providing a natural product for certain geometric metrics.

Findings

Defined a category of fibered corners manifolds with products

Introduced the 'ordered product' as a resolution of Cartesian products

Supported wedge and quasi-fibered boundary metrics including QAC and QALE

Abstract

Manifolds with fibered corners arise as resolutions of stratified spaces, in many body compactifications of vector spaces, moduli spaces, and other settings. We define a category of fibered corners manifolds which has products and transverse fiber products, generalizing both the resolutions of products of stratified spaces and many body products, which are special cases. The product in the fibered corners category is a resolution of the cartesian product by blow-up which we call the 'ordered product'. This ordered product is a natural product for wedge (aka incomplete edge) metrics and quasi-fibered boundary metrics, a class which includes QAC and QALE metrics.