Journal article 1241 views
Cyclic operad formality for compactified moduli spaces of genus zero surfaces
Transactions of the American Mathematical Society, Volume: 364, Issue: 11, Pages: 5881 - 5911
Swansea University Author: Jeffrey Giansiracusa
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DOI (Published version): 10.1090/S0002-9947-2012-05553-X
Abstract
The framed little 2-discs operad is homotopy equivalent to the Kimura-Stasheff-Voronov cyclic operad of moduli spaces of genus zero stable curves with tangent rays at the marked points and nodes. We show that this cyclic operad is formal, meaning that its chains and its homology (the Batalin-Vilkovi...
| Published in: | Transactions of the American Mathematical Society |
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| ISSN: | 0002-9947 1088-6850 |
| Published: |
AMS
2012
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa8375 |
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| Abstract: |
The framed little 2-discs operad is homotopy equivalent to the Kimura-Stasheff-Voronov cyclic operad of moduli spaces of genus zero stable curves with tangent rays at the marked points and nodes. We show that this cyclic operad is formal, meaning that its chains and its homology (the Batalin-Vilkovisky operad) are quasi-isomorphic cyclic operads. To prove this we introduce a new complex of graphs in which the differential is a combination of edge deletion and contraction, and we show that this complex resolves BV as a cyclic operad. |
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| Keywords: |
operad, cyclic operad, formality, Kontsevich graph complex, moduli space, Kimura-Stasheff-Voronov operad |
| College: |
Faculty of Science and Engineering |
| Issue: |
11 |
| Start Page: |
5881 |
| End Page: |
5911 |