PL cobordism and classification of PL manifolds

TL;DR

This paper advances the understanding of PL cobordism and classifies specific PL manifolds in dimensions 10 and 13 by computing related bordism groups.

Contribution

It provides new results on $C^*(PL)$, oriented PL cobordism, and computes string PL bordism groups for certain dimensions, aiding manifold classification.

Findings

Computed string PL bordism groups for specific dimensions

Classified PL manifolds in dimensions 10 and 13

Extended understanding of $C^*(PL)$ and PL cobordism

Abstract

In this paper, we present more conclusions for $C^\ast(\mathrm{PL})$ and oriented PL cobordism, and compute the string PL bordism groups of certain dimensions. Then, we apply these results to classify certain PL manifolds of dimensions $10$ and $13$.