# Imploded cross-sections

## TL;DR

This survey introduces imploded cross-sections to address non-symplectic cross-sections in Hamiltonian spaces, comparing their intersection homology with homology intersection spaces and computing related homologies.

## Contribution

It provides a comprehensive overview of imploded cross-sections and their homological properties, including explicit computations for specific geometric cases.

## Key findings

- Imploded cross-sections can be used to analyze Hamiltonian K-spaces.
- Intersection homology differs from homology intersection spaces in certain examples.
- Homology of intersection spaces for cones and suspensions of manifolds is explicitly computed.

## Abstract

In this survey article, we describe imploded cross-sections, which were developed in order to solve the problem that the cross-section of a Hamiltonian $K$-space is usually not symplectic. In some specific examples we contrast the intersection homology of some imploded cross-sections with their homology intersection spaces. Moreover, we compute the homology of intersection spaces associated to the open cone of a simply connected, smooth, oriented manifold and the suspension of such a manifold.