This was an invited opening plenary 1.5 hour talk at the international conference Glances @ Manifolds, low-&-high-dimensional, Jagiellonian University, Kraków, July 17-20, 2015, in which the main research results of the project group were presented.
B.04 Guest lectureCOBISS.SI-ID: 17374553
The theory skein modules is a relatively new branch of mathematics related to knot theory. Skein modules are algebraic objects, assign to any closed orientable 3-manifold that capture essential information about the geometry of the 3-manifold as they reflect the interaction between embedded 1-dimensional and 2-dimensional submanifolds. There is little known about the 3rd skein module since it has only been calculated for the simple case of the solid torus. The calculation for lens spaces has been announced at least two times hroughout history: in the 90s by Przytyski and Lambropoulou, and in 2013 by Diamantis and Lambropoulou, but the results were never published. In the conference our postdoc dr. Gabrovšek presented the long-awaited calculation of the 3rd skein module of lens spaces for the case of L(p,1). He presented the infinite basis and the isomorphism from the module to the free module, with this he showed that the module is freely generated with and infinite basis.
B.04 Guest lectureCOBISS.SI-ID: 17599321
The invited plenary talk was based on a joint paper with Bella and Tokgoz with the same title. In our talk we presented some of our new results, which came as a big surprise to several specialists from all around the world, taking part at the workshop, since they revealed several before unknown interconnections between classical combinatorial covering properties of remainders of topological groups and P-points. The latter have been intensively studied in recent decades. Following the talk there was a fruitful discussion with Arkhangelskii, the founder of this direction in the topological algebra. This confirms that the talk was well-received.
B.04 Guest lectureCOBISS.SI-ID: 17449817