Floer homology and covering spaces

Lidman, Tye¹ ; Manolescu, Ciprian²

¹ Department of Mathematics, North Carolina State University, Raleigh, NC, United States
² Department of Mathematics, UCLA, Los Angeles, CA, United States

Geometry & topology, Tome 22 (2018) no. 5, pp. 2817-2838.

Résumé

We prove a Smith-type inequality for regular covering spaces in monopole Floer homology. Using the monopole Floer/Heegaard Floer correspondence, we deduce that if a $3$–manifold $Y$ admits a $p^n$–sheeted regular cover that is a $\mathbb{Z}∕p\mathbb{Z}$–$L$–space (for $p$ prime), then $Y$ is a $\mathbb{Z}∕p\mathbb{Z}$–$L$–space. Further, we obtain constraints on surgeries on a knot being regular covers over other surgeries on the same knot, and over surgeries on other knots.

Détail

DOI : 10.2140/gt.2018.22.2817

Classification : 57R58, 57M10, 57M60
Keywords: Smith inequality, Seiberg–Witten, Heegaard Floer homology, virtually cosmetic, L–spaces

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