Abstract
AbstractFirst, we define the lattice cohomology associated with the link of a normal surface singularity, whenever this link is a rational homology sphere. This is done via the lattice of a resolution and well-chosen (Riemann-Roch type) weight functions of the lattice points. We prove that it is independent of all the choices and depends only on the link. The author conjectured that it is isomorphic as a graded Z[U]-module with the Heegaard Floer homology of the link (this fact was verified recently by Zemke). In parallel we define the graded roots as well as improvements of the 0-homology group. We compute this topological lattice cohomology and the graded root in many examples (star shaped graphs, surgery 3-manifolds). Then we discuss its path-version, the path lattice cohomology and its relationship with the geometric genus (of any analytic structure). In the final part we discuss the ‘analytic pair’: the analytic lattice cohomology. We compare the two theories and we test their behavior with respect to certain analytic deformations.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
