A colourful approach to string topology

Tarje Bargheer

A colourful approach to string topology

Tarje Bargheer

Institut for Matematiske Fag

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 operad
to be a coloured En􀀀1-operad. We twist this structure by the orthogonal
group SOpn 􀀀 1q to obtain an operad whose actions prescribe non-unital
pn 􀀀 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 the
extension is a simplication, and it adjoins a unit to the action on MSn.
We nally give advantages of our geometric stance on generalizing String
Topology even when N S1:We improve on equivariance of group actions on
MSn, and provide apparent links between Knot Theory and String Topology.

Originalsprog	Engelsk

Forlag	Faculty of Science, University of Copenhagen
Antal sider	103
Status	Udgivet - 2011

Citationsformater

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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.",

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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.

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