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Operads and embeddings

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posted on 2022-03-29, 03:12 authored by Florian De Leger
In this thesis, our objective is to present a strategy of a new proof of the weak equivalence Emb(R1, Rm) ∼ Ω2MapOp(D1,Dm), where Emb(R1, Rm) is the space of tangentially straightened long knots in Rm (see [1]) and MapOp(D1,Dm) is the space of operadic morphisms from the little 1-disk operad to the little m-disk operad. The existing proofs of Turchin [2] and Dwyer-Hess [1] are based on homotomy theory. We develop a more categorical proof which uses the theory of internal algebra classifiers [3] and explains conceptually the 'raison d'etre' of such a delooping. It also allows us to employ powerfu categorical/combinatorial techniques developed in [3] for proving and generalising of this sort of results. Our proof should admit a generalisation to higher dimensions, known as Dwyer-Hess conjecture.


Table of Contents

1. Introduction -- 2. Presentation of the existing results -- 3. Introduction to classifiers -- 4. New proof of delooping theorems


Theoretical thesis. Bibliography: pages 45-46

Awarding Institution

Macquarie University

Degree Type

Thesis MRes


MRes, Macquarie University, Faculty of Science and Engineering, Department of Mathematics

Department, Centre or School

Department of Mathematics

Year of Award


Principal Supervisor

Michael Batanin


Copyright Florian De Leger 2017 Copyright disclaimer: http://mq.edu.au/library/copyright




1 online resource (x, 46 pages)

Former Identifiers

mq:70760 http://hdl.handle.net/1959.14/1267463

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