Cross-connection semigroups amalgam of a vector bundle

TL;DR

This paper explores the structure of semigroup amalgams derived from cross-connection semigroups associated with the fibers of a vector bundle, extending the cross-connection framework to new algebraic constructs.

Contribution

It introduces the concept of semigroup amalgams of cross-connection semigroups specifically for the fibers of a vector bundle, expanding the application of cross-connection theory.

Findings

Describes the construction of semigroup amalgams from cross-connection semigroups.

Extends cross-connection representation to vector bundle fibers.

Provides a new algebraic framework for analyzing vector bundle structures.

Abstract

Cross-connections of normal categories was introduced by K.S.S.Nambooripad while discussing the structure of regular semigroups and via this cross-connections he obtained a beautiful representetion of regualr semigroup called the cross-connection semigroup (see cf.[4]). Subsequently cross-connection representation of various other semigroups such as concordant semigroups, semigroup of endomorphisms of a vector space are also described (cf.[6][5]). In this paper we describe the semigroup amalgam of cross-connection semigroups of the fibers of a vector bundle.