String Topology and Operad

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Akrami, Mahdi | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 47918 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Jafari, Amir
Abstract:
Let M be a closed manifold, oriented manifold of dimension -d. Let be the space of smooth loops in M. Chas and Sullivan defined a product on the homology H⋆(LM) of degree -d. They then investigated other structure that this product induces including a Batalin-Vilkovisky structure, and a lie algebra structure, and a lie algebra structure on the S1 equivariant homology HS1 ⋆ (LM). This algebraic structure as well as the others came under the general heading of the string topology of M
Keywords:
Operad ; Loop Homology ; String Homology ; Little Disk Operad ; Cocti Operad