A colourful approach to string topology
Publikation: Bog/antologi/afhandling/rapport › Ph.d.-afhandling › Forskning
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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
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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 „ Rn1 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 „ Rn1 we compute the cleavage operadto be a coloured En1-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 „ Rn1 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 „ Rn1 we compute the cleavage operadto be a coloured En1-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