Homotopy and root theory, manifold theory, stratified spaces, spherical space forms and topological dynamic systems.

• Grant number: 18/19603-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: October 01, 2018
• End date: September 30, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Oziride Manzoli Neto
• Grantee: Alexandre Thomas Guillaume Quesney
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 16/24707-4 - Algebraic, geometric and differential topology, AP.TEM

Abstract

Knot and link theory, a particular case of the theory of embeddings of manifolds into manifolds, took its origin from the attempt of classifying these topological objects (embeddings of the circle or disjoint union of it into the n-dimensional sphere).Along the time, various equivalence relations among the embeddings have been defined, and several invariants have been introduced. Recently, the study of string links, homotopy centres and topological field theories have lead to a new way of studying links. We pretend to make use of recent developments to study braids and links.

Scientific publications

(4)

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

MENCATTINI, IGOR; QUESNEY, ALEXANDRE; SILVA, PRYSCILLA. Post-symmetric braces and integration of post-Lie algebras. Journal of Algebra, v. 556, p. 547-580, AUG 15 2020. (18/19603-0)

KORINMAN, JULIEN; QUESNEY, ALEXANDRE. Classical shadows of stated skein representations at roots of unity. Algebraic and Geometric Topology, v. 24, n. 4, p. 61-pg., 2024-01-01. (18/19603-0)

KORINMAN, J.; QUESNEY, A.. The quantum trace as a quantum non-abelianization map. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, v. 31, n. 06, p. 49-pg., 2022-05-01. (18/19603-0)

MENCATTINI, IGOR; QUESNEY, ALEXANDRE. Crossed morphisms, integration of post-Lie algebras and the post-Lie Magnus expansion. COMMUNICATIONS IN ALGEBRA, v. 49, n. 8, p. 3507-3533, JUL 7 2021. (18/19603-0)