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We compute the $\operatorname{Pin}(2)$ -equivariant monopole Floer homology for the class of plumbed 3-manifolds considered by Ozsváth and Szabó [18]. We show that for these manifolds, the $\operatorname{Pin}(2)$ -equivariant monopole Floer homology can be calculated in terms of the Heegaard Floer/monopole Floer lattice complex defined by Némethi [15]. Moreover, we prove that in such cases the ranks of the usual monopole Floer homology groups suffice to determine both the Manolescu correction terms and the $\operatorname{Pin}(2)$ -homology as an Abelian group. As an application, we show that $\beta(-Y,s)=\bar{\mu}(Y,s)$ for all plumbed 3-manifolds with at most one “bad” vertex, proving (an analogue of) a conjecture posed by Manolescu [12]. Our proof also generalizes results by Stipsicz [21] and Ue [26] relating $\bar{\mu}$ with the Ozsváth–Szabó $d$ -invariant. Some observations aimed at extending our computations to manifolds with more than one bad vertex are included at the end of the paper.

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Dai, Irving - 

Id.: 71305353

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras clave57R58 - 

Tipo de recurso: Text  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Copyright 2018 The University of Michigan

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] 0026-2285
[References] 1945-2365

Fecha de contribución: 13-may-2018


* Michigan Math. J. 67, iss. 2 (2018), 423-447
* doi:10.1307/mmj/1523498585

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