Braids, links, cobordisms and formal groups

TL;DR

This paper explores the algebraic structures of braids, links, and cobordisms, connecting them with formal groups and manifold functions, and presents new methods and results in these areas.

Contribution

It introduces algebraic techniques linking braids and cobordisms with formal group theory, including an algorithm for Lazard's universal formal group.

Findings

Group theoretic results on braids and links

Infinitesimal braid group relations and connections

Applications of formal groups to cobordism theory

Abstract

V.V. Sharko in his papers and books has investigated functions on manifolds and cobordism. Braids intimately connect with functions on manifolds. These connections are represented by mapping class groups of corresponding discs, by fundamental groups of corresponding punctured discs, and by some other topological or algebraic structures. This paper presents selected algebraic methods and results of braids, links, cobordism connect with investigations by V.V. Sharko. These includes group theoretic results on braids and links, infinitesimal braid group relations and connections as well as connections on coherent sheaves on smooth schemes, a sketch of our algorithm for constructing of Lazard`s one dimensional universal commutative formal group and selected results on applications of commutative formal groups to cobordism theory.