Homological Type of Geometric Transitions

TL;DR

This paper introduces the concept of homological type to quantify topological changes caused by small and type II geometric transitions, advancing previous mathematical and physical results.

Contribution

It defines the homological type of a geometric transition and provides refined quantifications of topological changes beyond existing estimates.

Findings

Homological type effectively measures topological change.

Results align with and extend prior estimates.

Applicable to both mathematical and physical contexts.

Abstract

The present paper gives an account and quantifies the change in topology induced by small and type II geometric transitions, by introducing the notion of the \emph{homological type} of a geometric transition. The obtained results agree with, and go further than, most results and estimates, given to date by several authors, both in mathematical and physical literature.