Exact fillings using universal covers in Floer theory
Abstract
We study exact fillings of Legendrians and contact manifolds using Floer theory of universal covers. We prove vanishing results on wrapped Floer homology of the universal cover and symplectic (co)homology with k[π1] coefficients by using lifted versions of Ritter's TQFT operations. We use these results to show that an exact Maslov zero Lagrangian filling of the standard Legendrian Λstd in any Liouville filling of (S2n−1,ξstd) is diffeomorphic to a ball in dimension at least 5. We show that the existence of a topological simple exact filling W with vanishing symplectic homology for a dynamically convex contact manifold M2n−1 reveals information about homotopy groups of W and M. We also strengthen a theorem of Zhou for ADC-contact manifolds as an application of universal covers.
Related
- Exact triangle and spectral sequence of the equivariant Floer homology of double branched covers
- Exact orbifold fillings of contact manifolds
- Surgery Exact Triangles in Involutive Heegaard Floer Homology
- Floer-theoretic entropy of exact symplectomorphisms
- Finite Cyclic Fundamental Groups and Exotic Universal Covers from the Cartwright--Steger Surface
BibTeX
@misc{shahul2026exact,
title = {{Exact fillings using universal covers in Floer theory}},
author = {Shahnaz Shamim Shahul},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10078},
eprint = {2610.10078},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10078},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Exact fillings using universal covers in Floer theory
AU - Shahnaz Shamim Shahul
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10078
UR - https://arxiv.org/abs/2610.10078
AB - We study exact fillings of Legendrians and contact manifolds using Floer theory of universal covers. We prove vanishing results on wrapped Floer homology of the universal cover and symplectic (co)homology with k[π_1] coefficients by using lifted versions of Ritter's TQFT operations. We use these results to show that an exact Maslov zero Lagrangian filling of the standard Legendrian Λ_std in any Liouville filling of (S^2n−1,ξ_std) is diffeomorphic to a ball in dimension at least 5. We show that the existence of a topological simple exact filling W with vanishing symplectic homology for a dynamically convex contact manifold M^2n−1 reveals information about homotopy groups of W and M. We also strengthen a theorem of Zhou for ADC-contact manifolds as an application of universal covers.
ER -