https://pages.uoregon.edu/lipshitz/bfh/index.html A bordered Heegaard Floer computation package Hugo en-us lipshitz@uoregon.edu (Robert Lipshitz) lipshitz@uoregon.edu (Robert Lipshitz) https://pages.uoregon.edu/lipshitz/bfh/mathematics/index.html Mon, 01 Jan 0001 00:00:00 +0000lipshitz@uoregon.edu (Robert Lipshitz) https://pages.uoregon.edu/lipshitz/bfh/mathematics/index.html The mathematics underlying bfh_python This is a brief introduction to bordered Floer homology and Zhan’s extension of it, to help with using the bfh_python package. For more details, see the references below. The basics bfh_python computes HF-hat by a divide and conquer algorithm. Roughly, to a closed surface F it associates a differential algebra A(F). To a 3-manifold Y with boundary F, it associates a right A(F)-module CFA(Y) and a left A(-F)-module CFD(Y). More generally, to a 3-dimensional cobordism Y from F1 to F2 it associates a bimodule CFDA(Y). https://pages.uoregon.edu/lipshitz/bfh/structure/index.html Mon, 01 Jan 0001 00:00:00 +0000lipshitz@uoregon.edu (Robert Lipshitz) https://pages.uoregon.edu/lipshitz/bfh/structure/index.html The structure of the bfh_python package The goal of this page is to try to explain the design philosophy (as I understand it) underlying bfh_python, and some of the packages and classes that are most likely to be useful. Before that, two general pieces of advice. First, most classes and functions have docstrings, which say a little about what they are for and/or how to use them. Some are more extensive than others. Second, all of the modules have a corresponding test module. For example, the pmc.py module (which encodes pointed matched circles and the algebras associated to them) has an associated test module pmctest.py. Looking at the test module is often the easiest way to figure out how to use the various classes, and how they behave. (Of course, you can also use these test modules to test that bfh_python is installed and working properly; you can run all the test modules by running python regression.py.) https://pages.uoregon.edu/lipshitz/bfh/further/index.html Mon, 01 Jan 0001 00:00:00 +0000lipshitz@uoregon.edu (Robert Lipshitz) https://pages.uoregon.edu/lipshitz/bfh/further/index.html Relative gradings and spinc structures bfh_python computes the decomposition of HF-hat into spinc-structures and the relative Maslov grading in each spinc-structure. It also computes the relative, rational Maslov grading between torsion spinc-structures, and the ambiguity of the Maslov grading in non-torsion spinc-structures (the divisibility of the first Chern class). A lens space from dstructure import infTypeD, zeroTypeD from pmc import splitPMC from arcslide import Arcslide from arcslideda import ArcslideDA Z = splitPMC(1) solid_torus = infTypeD(1) tau_m = ArcslideDA(Arcslide(Z,1,2)) tau_l = ArcslideDA(Arcslide(Z,2,1)) slides = [tau_m, tau_m, tau_l, tau_l] for s in slides: solid_torus = s.tensorD(solid_torus) oth_side = zeroTypeD(1) cf = oth_side.morToD(solid_torus) cf.simplify() print(len(cf)) To get the relative gradings: