Paper 11

The Geometry of UK Career Inequality: Topology, Regimes, and Mobility Boundaries

Stage 0 – Foundation In Progress Journal of the Royal Statistical Society, Series A (target)

Abstract

This paper gives an applied, substantive account of the geometry of UK career inequality, using topological data analysis on long-run employment histories from the British Household Panel Survey and Understanding Society. Rather than treating mobility as movement along a one-dimensional ladder, we characterise the *shape* of trajectory space: the regimes into which careers fall, the boundaries between those regimes that operate as mobility barriers, and the sub-populations whose career shapes diverge from the dominant clusters. Persistent homology establishes that the trajectory structure exceeds memoryless null expectations; Mapper exposes the interior organisation of that structure, including precarious cycling groups and a gendered early-exit branch. The paper is the applied (Series A) companion to a methodological treatment of the same data; it is assembled from, and supersedes, the earlier core persistent-homology and Mapper papers in this programme.

Plain-Language Summary

Careers are usually described as movement up or down a ladder. This paper argues that the space of possible working lives has a richer shape — clusters of similar careers, and boundaries between them that most people never cross. Using decades of UK household survey data, it maps that shape and shows where the hard borders to mobility lie, and which groups (in particular, women leaving paid work early) follow career shapes that standard mobility statistics miss entirely.

Programme note. This paper is the applied (Series A) half of a companion pair, assembled in April 2026 as part of a strategic reorganisation of the research programme. It draws its applied content from the earlier core persistent-homology paper and the Mapper paper, both of which it supersedes (see Papers 1–3). The methodological machinery it relies on is developed in its Series B companion, Structured Hypothesis Testing for Persistent Homology of Longitudinal Social Data (Paper 12).

Overview

The paper treats a working life as a trajectory through a space of employment states, observed over up to three decades of UK panel data, and asks what shape the collection of such trajectories has. The substantive claim is that career inequality is not adequately described as position on a one-dimensional mobility scale. It is better described as location within a structured geometry of regimes, separated by boundaries that are rarely crossed.

Status

This is an active draft (in-progress, Stage 0), in lockstep revision with its Series B companion. Several results remain under analysis and are not reported here as settled findings; the page will be updated as the manuscript stabilises toward submission.

Key Findings

Methods

Computational Requirements

Hardware
CPU
⏱ Runtime
Hours

Position in Research Programme

■ This paper

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