TY - JOUR

T1 - The cleavage operad and string topology of higher dimension

AU - Bargheer, Tarje

N1 - Publisher Copyright:
© 2014 American Mathematical Society.

PY - 2014

Y1 - 2014

N2 - For a manifold N embedded inside euclidean space ℝn+1, we produce a coloured operad that acts on the space of maps from N to M, where M is a compact, oriented, smooth manifold. Our main example of interest is N, the unit sphere, and we indicate how this gives homological actions, generalizing the action of the spineless cacti operad and retrieving the Chas-Sullivan product by taking N to be the unit circle in ℝ2. We go on to show that for Sn, the unit sphere in ℝn+1, the operad constructed is a coloured En+1-operad. This En+1-structure is finally twisted by SO(n + 1) to homologically agree with actions of the operad of framed little (n + 1)-disks.

AB - For a manifold N embedded inside euclidean space ℝn+1, we produce a coloured operad that acts on the space of maps from N to M, where M is a compact, oriented, smooth manifold. Our main example of interest is N, the unit sphere, and we indicate how this gives homological actions, generalizing the action of the spineless cacti operad and retrieving the Chas-Sullivan product by taking N to be the unit circle in ℝ2. We go on to show that for Sn, the unit sphere in ℝn+1, the operad constructed is a coloured En+1-operad. This En+1-structure is finally twisted by SO(n + 1) to homologically agree with actions of the operad of framed little (n + 1)-disks.

UR - http://www.scopus.com/inward/record.url?scp=84924778429&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-2014-05946-1

DO - 10.1090/S0002-9947-2014-05946-1

M3 - Article

SN - 0002-9947

VL - 366

SP - 4209

EP - 4241

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 8

ER -