Gardado en:
| Autor Principal: | |
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| Formato: | Preprint |
| Publicado: |
2020
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| Subjects: | |
| Acceso en liña: | https://arxiv.org/abs/2004.07362 |
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Table of Contents:
- We extend a CDGA $V$ with a perfect pairing of degree $n$ on cohomology to a CDGA $\hat V$ with a pairing of degree $n$ on chain level such that $\hat V$ admits a Hodge decomposition and retracts onto $V$ preserving the pairing on cohomology; here we suppose that $V$ is either 1-connected, or that $V$ is connected, of finite type, and $n$ is odd. We show that a Hodge decomposition of $\hat V$ induces a differential Poincaré duality model of $V$ in a natural way. Assuming that $H(V)$ is 1-connected, we apply our extension to a Sullivan model of $V$ in the proof of the existence and "uniqueness" of a 1-connected differential Poincaré duality model of $V$ by Lambrechts & Stanley; we eliminate their extra assumptions in the uniqueness statement, including $H^2(V)=0$ if $n$ is odd.