math.GT daily digest: 2 new submissions for 29 June 2026

Contact cosmetic surgery on Legendrian knots in integer homology sphere -spaces

• Authors: Apratim Chakraborty; Swarup Kumar Das; Tanushree Shah
• arXiv: 2606.27485 2
• Subjects: Geometric Topology (math.GT)
• Comments: Comments are welcome! arXiv admin note: text overlap with arXiv:2411.02201

We extend the study of contact cosmetic surgeries to Legendrian knots in integer homology sphere L-spaces . We prove that the contact cosmetic surgery conjecture holds for all non-trivial Legendrian knots in this setting, with the possible exception of Lagrangian slice knots. Our argument adapts and refines techniques from the S3 case to the broader context of L-spaces, incorporating constraints arising from Heegaard Floer theory

Infinite ECH Capacities and Anosov Flows

• Authors: Gabriel Beiner
• arXiv: 2606.28316 3
• Subjects: Symplectic Geometry (math.SG); Dynamical Systems (math.DS); Geometric Topology (math.GT)
• Comments: 49 pages, 3 figures, comments welcome

This article relates the theory of embedded contact homology (ECH) with the dynamics of Anosov flows. We show that in many cases the ECH capacities of a symplectic 4-manifold are infinite, including cotangent disk bundles over closed oriented surfaces of genus at least two. We prove that ECH obstructs Reeb Anosov and Hamiltonian Anosov flows, addressing the four-dimensional case of a question posed by Herman in 1998. Further, we obtain Floer-theoretic obstructions to a 3-manifold admitting any Anosov flow. As an application, we give new constraints on the existence of embedded Lagrangians of genus at least two in symplectic 4-manifolds. In an appendix, some related results in all dimensions are proved for capacities constructed from rational symplectic field theory.