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The top homology group of the genus 3 Torelli group
Journal of Topology. 2023. Vol. 16. No. 3. P. 1048–1092.
Spiridonov I.
Morozov A., Russian Journal of Nonlinear Dynamics 2021 Vol. 17 No. 4 P. 465–473
According to the Nielsen-Thurston classification, the set of homotopy classes of orientation-preserving homeomorphisms of orientable surfaces is split into four disjoint subsets. Each subset consists of homotopy classes of homeomorphisms of one of the following types:
T1) periodic homeomorphism;
T_2) reducible non-periodic
homeomorphism of algebraically finite order;
T_3) a reducible homeomorphism that is not a homeomorphism of algebraically finite order;
T_4) pseudo-Anosov homeomorphism.
It is ...
Added: December 14, 2021
Bychkov B., Kazakov A., Talalaev D., Теоретическая и математическая физика 2021 Т. 207 № 2 С. 594–603
We construct a generalization of the Tutte polynomial for vertex-weighted graphs for which the coefficients of the “deletion–contraction” relation depend nontrivially on the vertex weights. We show that the corresponding relation on the coefficients coincides with the two-cocycle relation in the group cohomology. We obtain a representation of a new invariant by summing over subgraphs ...
Added: July 7, 2021
Katzarkov L. V., Akhmedov A., Advances in Mathematics 2020 Vol. 360 P. 1–23
We define a new 4-dimensional symplectic cut and paste operations arising from the generalized star relations (ta0ta1ta2⋯ta2g+1)2g+1=tb1tb2gtb3, also known as the trident relations, in the mapping class group Γg,3 of an orientable surface of genus g≥1 with 3 boundary components. We also construct new families of Lefschetz fibrations by applying the (generalized) star relations and the chain relations to the families of words (tc1tc2⋯tc2g−1tc2gtc2g+12tc2gtc2g−1⋯tc2tc1)2n=1, (tc1tc2⋯tc2gtc2g+1)(2g+2)n=1and (tc1tc2⋯tc2g−1tc2g)2(2g+1)n=1 in the ...
Added: May 19, 2020