A colourful approach to string topology

Publikation: Bog/antologi/afhandling/rapport › Ph.d.-afhandling › Forskning

Standard

A colourful approach to string topology. / Bargheer, Tarje.

Faculty of Science, University of Copenhagen, 2011. 103 s.

Publikation: Bog/antologi/afhandling/rapport › Ph.d.-afhandling › Forskning

Harvard

Bargheer, T 2011, A colourful approach to string topology. Faculty of Science, University of Copenhagen.

APA

Bargheer, T. (2011). A colourful approach to string topology. Faculty of Science, University of Copenhagen.

Vancouver

Bargheer T. A colourful approach to string topology. Faculty of Science, University of Copenhagen, 2011. 103 s.

Author

Bargheer, Tarje. / A colourful approach to string topology. Faculty of Science, University of Copenhagen, 2011. 103 s.

Bibtex

@phdthesis{21c2e4da41324fd988a548f2ac6a9400,
title = "A colourful approach to string topology",
abstract = "For M a compact, orientable manifold and N „ Rn􀀀1 a submanifold, we construct the cleavage operad that acts on MN through correspondences,analogous to the Cacti Operad acting on MS1 , formulating String Topology.For the unit sphere, N : Sn „ Rn􀀀1 we compute the cleavage operadto be a coloured En􀀀1-operad. We twist this structure by the orthogonalgroup SOpn 􀀀 1q to obtain an operad whose actions prescribe non-unitalpn 􀀀 1q-Batalin-Vilkovisky algebras. We show that the action through correspondences transfers to a spectral action on MSn ^ SdimpMq. This action is obtained through an extension of the Cleavage Operad. Homotopically theextension is a simplication, and it adjoins a unit to the action on MSn.We nally give advantages of our geometric stance on generalizing StringTopology even when N S1:We improve on equivariance of group actions onMSn, and provide apparent links between Knot Theory and String Topology.",
author = "Tarje Bargheer",
year = "2011",
language = "English",
publisher = "Faculty of Science, University of Copenhagen",

}

RIS

TY - BOOK

T1 - A colourful approach to string topology

AU - Bargheer, Tarje

PY - 2011

Y1 - 2011

N2 - For M a compact, orientable manifold and N „ Rn􀀀1 a submanifold, we construct the cleavage operad that acts on MN through correspondences,analogous to the Cacti Operad acting on MS1 , formulating String Topology.For the unit sphere, N : Sn „ Rn􀀀1 we compute the cleavage operadto be a coloured En􀀀1-operad. We twist this structure by the orthogonalgroup SOpn 􀀀 1q to obtain an operad whose actions prescribe non-unitalpn 􀀀 1q-Batalin-Vilkovisky algebras. We show that the action through correspondences transfers to a spectral action on MSn ^ SdimpMq. This action is obtained through an extension of the Cleavage Operad. Homotopically theextension is a simplication, and it adjoins a unit to the action on MSn.We nally give advantages of our geometric stance on generalizing StringTopology even when N S1:We improve on equivariance of group actions onMSn, and provide apparent links between Knot Theory and String Topology.

AB - For M a compact, orientable manifold and N „ Rn􀀀1 a submanifold, we construct the cleavage operad that acts on MN through correspondences,analogous to the Cacti Operad acting on MS1 , formulating String Topology.For the unit sphere, N : Sn „ Rn􀀀1 we compute the cleavage operadto be a coloured En􀀀1-operad. We twist this structure by the orthogonalgroup SOpn 􀀀 1q to obtain an operad whose actions prescribe non-unitalpn 􀀀 1q-Batalin-Vilkovisky algebras. We show that the action through correspondences transfers to a spectral action on MSn ^ SdimpMq. This action is obtained through an extension of the Cleavage Operad. Homotopically theextension is a simplication, and it adjoins a unit to the action on MSn.We nally give advantages of our geometric stance on generalizing StringTopology even when N S1:We improve on equivariance of group actions onMSn, and provide apparent links between Knot Theory and String Topology.

M3 - Ph.D. thesis

BT - A colourful approach to string topology

PB - Faculty of Science, University of Copenhagen

ER -

ID: 40718566