A dendroidal approach to Goodwillie-Weiss manifold calculus

Miguel Lourenço Henriques Barata

doi:10.33540/3271

A dendroidal approach to Goodwillie-Weiss manifold calculus

Miguel Lourenço Henriques Barata

Sub Fundamental Mathematics

Research output: Thesis › Doctoral thesis 1 (Research UU / Graduation UU)

Abstract

In this thesis we prove that the homotopy theory of simplicial operadic right modules can be captured by the formalism of right fibrations of forest spaces over an operad. Using this language, we recover the Goodwillie-Weiss tower for embedding spaces, together with a description of its layers.

Original language	English
Qualification	Doctor of Philosophy
Awarding Institution	Utrecht University
Supervisors/Advisors	Moerdijk, Ieke, Supervisor Heuts, Gijs, Co-supervisor
Award date	10 Dec 2025
Place of Publication	Utrecht
Publisher	Utrecht University
Print ISBNs	978-90-393-7966-0
DOIs	https://doi.org/10.33540/3271
Publication status	Published - 10 Dec 2025

Keywords

Homotopy theory
Algebraic topology
Operad

Access to Document

10.33540/3271

A dendroidal approach to Goodwillie-Weiss manifold calculusFinal published version, 1.66 MB

Cite this

@phdthesis{c0370fdf27e340879d16695abb5d175a,

title = "A dendroidal approach to Goodwillie-Weiss manifold calculus",

abstract = "In this thesis we prove that the homotopy theory of simplicial operadic right modules can be captured by the formalism of right fibrations of forest spaces over an operad. Using this language, we recover the Goodwillie-Weiss tower for embedding spaces, together with a description of its layers.",

keywords = "Homotopietheorie, Algebra{\"i}sche topologie, Operad, Homotopy theory, Algebraic topology, Operad",

author = "\{Louren{\c c}o Henriques Barata\}, Miguel",

year = "2025",

month = dec,

day = "10",

doi = "10.33540/3271",

language = "English",

isbn = "978-90-393-7966-0",

publisher = "Utrecht University",

type = "Doctoral thesis 1 (Research UU / Graduation UU)",

school = "Universiteit Utrecht",

}

TY - THES

T1 - A dendroidal approach to Goodwillie-Weiss manifold calculus

AU - Lourenço Henriques Barata, Miguel

PY - 2025/12/10

Y1 - 2025/12/10

N2 - In this thesis we prove that the homotopy theory of simplicial operadic right modules can be captured by the formalism of right fibrations of forest spaces over an operad. Using this language, we recover the Goodwillie-Weiss tower for embedding spaces, together with a description of its layers.

AB - In this thesis we prove that the homotopy theory of simplicial operadic right modules can be captured by the formalism of right fibrations of forest spaces over an operad. Using this language, we recover the Goodwillie-Weiss tower for embedding spaces, together with a description of its layers.

KW - Homotopietheorie

KW - Algebraïsche topologie

KW - Operad

KW - Homotopy theory

KW - Algebraic topology

KW - Operad

U2 - 10.33540/3271

DO - 10.33540/3271

M3 - Doctoral thesis 1 (Research UU / Graduation UU)

SN - 978-90-393-7966-0

PB - Utrecht University

CY - Utrecht

ER -

A dendroidal approach to Goodwillie-Weiss manifold calculus

Abstract

Keywords

Access to Document

Fingerprint

Cite this