Zoran Skoda fol-lit

A partial bibliography related to a proposal centered on geometry of foliations, Spring 2021; non-cleaned additions at fol-lit2. See also foliation, Haefliger groupoid and Rankin-Cohen bracket.

• A. Agrachev and Y. Sachkov, Control Theory from the Geometric Viewpoint. Springer 2004.

• I. Androulidakis and G. Skandalis. The holonomy groupoid of a singular foliation. J. Reine Andew. Math. 626 (2009) 1–37.

• Ya.V. Bazaikin, A.S. Galaev, Losik classes for codimension one foliations. J. Inst. Math. Jussie, 1-29, arXiv:1810.01143 doi

• Ya.V. Bazaikin, A.S. Galaev, and P. Gumenyuk, Non-diffeomorphic Reeb foliations and modified Godbillon-Vey class, arXiv:1912.01267.

• Ya.V. Bazaikin, A.S. Galaev, N.I. Zhukova. Chaos in Cartan foliations. CHAOS 30 (2020), no. 10, 103116.

• R. Bott, A. Haefliger On characteristic classes of $\Gamma$-foliations. Bull. AMS, 78 (1972), 1039–1044.

• R. Bott, On characteristic classes in the framework of Gelfand-Fuks cohomology. Colloque analyse et topologie, Astérisque, no. 32-33 (1976), 27 p.

• H. Bursztyn, A. Cabrera, M. del Hoyo, Vector bundles over Lie groupoids and algebroids. Adv. Math. 290 (2016), 163–207.

• D. Calegari, Foliations and the Geometry of 3-Manifolds. Oxford University Press. 2007

• A. Candel and L. Conlon, Foliations II, Amer. Math. Soc., Providence, RI, 2003.

• A. Connes, Noncommutative Geometry. Academic Press 1994.

• B. L. Feigin, Characteristic classes of flags of foliations. Funct. Anal. Appl., 9 (1975)

• A. S. Galaev, Comparison of approaches to characteristic classes of foliations, arXiv:1709.05888.

• I. M. Gelfand, The cohomology of infinite dimensional Lie algebras; some questions of integral geometry, Actes, Congr`es intern. Math., 1970. Tome 1, pp. 95–111.

• A. Hamasaki, Continuous cohomologies of Lie algebras of formal $G$-invariant vector fields and obstructions to lifting foliations. Publ. RIMS, Kyoto Univ. 20 (1984), 401–429.

• A. Hamasaki, Cohomologies of Lie algebras of formal vector fields preserving a foliation. Publ. Res. Inst. Math. Sci. 24 (1988), 639-652.

• M. Henneaux, C. Teitelboim, Quantization of Gauge Systems, Princeton Univ. 1992.

• S. Hurder, Dynamics and the Godbillon-Vey class: a History and Survey, In Foliations: Geometry and Dynamics, World Sci. Pub. Co. Inc., River Edge, N.J., 2002, 29–60.

• S. Hurder and R. Langevin, Dynamics and the Godbillon-Vey class of $C^1$ foliations, J. Math. Soc. Japan 70 (2018), no. 2, 423–462, arXiv:1403.0494

• V. Jurdjevic, Geometric Control Theory. Cambridge Univ. Press, 1997.

• F.W. Kamber, Ph. Tondeur, Foliated bundles and characteristic classes, Lecture Notes in Mathematics, Vol. 493, Springer-Verlag, Berlin-New York, 1975.

• A. Katok, B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems. Cambridge Univ. Press, 1995.

• A. S. Khoroshkin, Lie algebra of formal vector fields extended by formal g-valued functions. J. Math. Sci. (N. Y.) 143 (2007) 2816–2830.

• A. S. Khoroshkin, Characteristic classes of flags of foliations and Lie algebra cohomology. Transformation Groups 21 (2016) 479–518.

• M. Kontsevich, Rozansky-Witten invariants via formal geometry. Compos. Math. 115 (1999).

• M. Kontsevich, Formal (non)-commutative symplectic geometry, The Gelfand Mathematical. Seminars, 1990-1992, Ed. L.Corwin, I.Gelfand, J.Lepowsky, Birkhauser 1993, 173–187.

• A. Kotov, M. Grigoriev, Gauge PDE and AKSZ–type sigma models, Fortschr. Phys. 67 (2019)

• A. Kotov, T. Strobl, Curving Yang-Mills-Higgs gauge theories, Phys. Rev. D 92 (2015)

• A. Kotov, T. Strobl, Gauging without initial symmetry, J. Geom. Phys. 99, 184–189 (2016)

• A. Kotov, T. Strobl, Integration of quadratic Lie algebroids to Riemannian Cartan-Lie groupoids, Lett. Math. Phys. 108 (3), 737–756 (2018)

• A. Kotov, T. Strobl, Lie algebroids, gauge theories, and compatible geometrical structures, Reviews in Mathematical Physics 31(4), 1950015 (31 pages), 2019.

• A. Kotov, T. Strobl, Universal Cartan-Lie algebroid of an anchored bundle with connection and compatible geometries, J. Geom. Phys. 135, 1–6 (January 2019)

• C. Laurent-Gengoux, S. Lavau, T. Strobl. The universal Lie $\infty$-algebroid of a singular foliation, arXiv:1806.00475

• A. Giaquinto, J. J. Zhang, Bialgebras, twists and deformation formulas, J. Pure Appl. Alg. 128 (1998) 133–151, arXiv:hep-th/9411140

• J.A. L'opez, H. Nozawa. Secondary characteristic classes of transversely homogeneous foliations. arXiv:1205.3375v4

• M. V. Losik, A certain generalization of a manifold and its characteristic classes. Funct. Anal. Appl. 24 (1990), no. 1, 26–32

• M.V. Losik, Categorical differential geometry, Cah. Top. G'eom. Diff. Cat. 35 (1994) 274–290.

• M.V. Losik, Orbit spaces and leaf spaces of foliations as generalized manifolds, arXiv:1501.04993

• T. Machon, The Godbillon-Vey invariant as topological vorticity compression and obstruction to steady flow in ideal fluids. Proc. Royal Sci. A-Math. 476 (2020)

• T. Machon, The Godbillon-Vey invariant as a restricted Casimir of three-dimensional ideal fluids. J. Phys. A-Math. Teor. 53 (2020)

• V. E. Marotta, R. J. Szabo, Born sigma-models for para-Hermitian Manifolds and generalized T-duality, arXiv:1910.09997

• D. Meljanac, S. Meljanac, Z. Škoda, R. Štrajn, Interpolations between Jordanian twists, the Poincar'e-Weyl algebra and dispersion relations, Int. J. Mod. Phys. A 35:8 (2020) 2050034

• S. Meljanac, Z. Škoda, M. Stojić, Lie algebra type noncommutative phase spaces are Hopf algebroids, Lett. Math. Phys. 107:3, 475–503 (2017); D. Pištalo, Z. Škoda, Exponential map and realizations for Lie groupoids, in preparation; S. Meljanac, Z. Škoda, Hopf algebroid twists for deformation quantization of linear Poisson structures, SIGMA 14 (2018), 026.

• I. Moerdijk, Models for the leaf space of a foliation, Eur. Cong. Math. 2000, vol. I, 481–489. (Barcelona), Progr. Math., 201, Birkhauser, Basel, 2001.

• T. Mizutani, S. Morita and T. Tsuboi, The Godbillon-Vey classes of codimension one foliations which are almost without holonomy, Annals Math. 113 (1981), 515–527.

• S. Morita and T. Tsuboi, The Godbillon-Vey class of codimension one foliations without holonomy, Topology, 19 (1980), 43–49.

• P. Molino, Riemannian foliations, Progr. Math. 73, Boston, 1988.

• A. Navas, Groups of Circle Diffeomorphisms. Univ. Chicago Press. 2011.

• D. Nolte, Introduction to Modern Dynamics: Chaos, Networks, Space and Time. Oxford~2015.

• R. Rochberg, X. Tang, Y. Yao, A survey of Rankin-Cohen deformations, Perspectives on Noncommutative Geometry, Fields Inst. Commun. 61:7 (2011) arXiv:0909.4364

• G. Teschl, Ordinary Differential Equations and Dynamical Systems. Providence: AMS 2012.

• A.M. Torpe, K-theory for the leaf space of foliations by Reeb components, J. Func. Anal. 61 (1985) 15–71.

• W. Thurston, Non-cobordant foliations on $S^3$. Bulletin Amer. Math. Soc. 78 (1972), 511–514.

• I. Vaisman, Lectures on geometry of Poisson manifolds. Springer, 1994.

• P. Walczak, Dynamics of Foliations, Groups and Pseudogroups. Springer, 2004.

• G. M. Webb, A. Prasad, S.C. Anco, et al. Godbillon-Vey helicity and magnetic helicity in magnetohydrodynamics. J. Plasma Phys. 85 (2019)