Parallizable manifolds and the fundamental group

ntroduction. Low-dimensional topology is dominated by the fundamental group. However, since every finitely presented group is the fundamental group of some closed 4-manifold, it is often stated that the effective influence of π1 ends in dimension three. This is not quite true, however, and there are some interesting border disputes. In this paper, we show that, by imposing the extra condition of parallelizability on the tangent bundle, the dominion of π1 is extended by an extra dimension

Timelike duality, M′M'-theory and an exotic form of the Englert solution

Through timelike dualities, one can generate exotic versions of $M$-theory with different spacetime signatures. These are the $M^*$-theory with signature $(9,2,-)$, the $M'$-theory, with signature $(6,5,+)$ and the theories with reversed signatures $(1,10, -)$, $(2,9, +)$ and $(5,6, -)$. In $(s,t, \pm)$, $s$ is the number of space directions, $t$ the number of time directions, and $\pm$ refers to the sign of the kinetic term of the $3$ form. The only irreducible pseudo-riemannian manifolds admitting absolute parallelism are, besides Lie groups, the seven-sphere $S^7 \equiv SO(8)/SO(7)$ and its pseudo-riemannian version $S^{3,4} \equiv SO(4,4)/SO(3,4)$. [There is also the complexification $SO(8,\mathbb{C})/SO(7, \mathbb{C})$, but it is of dimension too high for our considerations.] The seven-sphere $S^7\equiv S^{7,0}$ has been found to play an important role in $11$-dimensional supergravity, both through the Freund-Rubin solution and the Englert solution that uses its remarkable parallelizability to turn on non trivial internal fluxes. The spacetime manifold is in both cases $AdS_4 \times S^7$. We show that $S^{3,4}$ enjoys a similar role in $M'$-theory and construct the exotic form $AdS_4 \times S^{3,4}$ of the Englert solution, with non zero internal fluxes turned on. There is no analogous solution in $M^*$-theory.Comment: 18 pages, v2: typos fixe

NL4Py: Agent-Based Modeling in Python with Parallelizable NetLogo Workspaces

NL4Py is a NetLogo controller software for Python, for the rapid, parallel execution of NetLogo models. NL4Py provides both headless (no graphical user interface) and GUI NetLogo workspace control through Python. Spurred on by the increasing availability of open-source computation and machine learning libraries on the Python package index, there is an increasing demand for such rapid, parallel execution of agent-based models through Python. NetLogo, being the language of choice for a majority of agent-based modeling driven research projects, requires an integration to Python for researchers looking to perform statistical analyses of agent-based model output using these libraries. Unfortunately, until the recent introduction of PyNetLogo, and now NL4Py, such a controller was unavailable. This article provides a detailed introduction into the usage of NL4Py and explains its client-server software architecture, highlighting architectural differences to PyNetLogo. A step-by-step demonstration of global sensitivity analysis and parameter calibration of the Wolf Sheep Predation model is then performed through NL4Py. Finally, NL4Py's performance is benchmarked against PyNetLogo and its combination with IPyParallel, and shown to provide significant savings in execution time over both configurations