Toric Topology studies torus actions on manifolds and cell complexes whose orbit quotients have a rich combinatorial structure. The subject has appeared in the late 1990s as a topological extension of the theory of algebraic and hamiltonian toric manifolds. Toric Topology is characterised by a confluence of ideas and methodology of equivariant topology, algebraic and symplectic geometry, combinatorics, commutative and homological algebra. This is a new and actively developing area attracting more and more researchers around the world.

• Overview presentation on combinatorial and toric topology, by V.Buchstaber, A.Gaifullin and T.Panov (pdf-file with animations)

• В.М.Бухштабер, Т.Е.Панов. Торическая топология. Современные проблемы математики и механики, т.III "Математика", вып.1. Посвящается 70-летию со дня рождения В.А.Садовничего. Изд-во Московского Университета, 2009, стр. 109--120 (in Russian). pdf-файл

• Victor M. Buchstaber and Nigel Ray. An Invitation to Toric Topology: Vertex Four of a Remarkable Tetrahedron. In Toric Topology (M.Harada et al, eds.). Contemp. Math., vol.460, American Mathematical Society, Providence, RI, 2008, pp.1--27; pdf (preprint version)

• В.М.Бухштабер, Т.Е.Панов. Торические действия в топологии и комбинаторике. Издательство МЦНМО, Москва, 2004 (272 стр.) (in Russian)

• Victor M. Buchstaber and Taras E. Panov. Torus Actions and Their Applications in Topology and Combinatorics. University Lecture Series, vol.24, American Mathematical Society, Providence, RI, 2002 (152 pages). pdf (preprint version)

• A toric topology section within the International Conference ``Geometric Toplogy, Discrete Geometry and Number Theory'', L.V.Keldysh Centenary (Moscow, August 2004)
• International Сonference on Toric Topology (Osaka, Japan, 29 May-3 June 2006)
• A toric topology section within the International Conference ``Differential Equations and Topology'', L.S.Pontrjagin Centenary (Moscow, June 2008)
• International Conference ``New Horizons in Toric Topology'' (Manchester, U.K., 7--11 July 2008)
• A toric topology section within the International Conference "Geometry, Topology, Algebra and Number Theory, Applications" dedicated to the 120th anniversary of Boris Delone (Moscow, 16-20 August 2010)
• International Conference "Toric Methods in Homotopy Theory and Related Subjects" (Queen's University Belfast, UK, 18-20 July 2011).
• International Conference "Toric Topology and Autormorphic Functions" (Khabarovsk, Russia, 5-10 September 2011)
• International Meeting "Toric Topology 2011 in Osaka" (Osaka, Japan, 28-30 November 2011)

• The Manchester Toric Topology Page

• Research proposal by T.Panov on toric topology for 2007-2009, supported by the grant of the Pierre Deligne Foundation of 2006: English summary, proposal (in Russian)

• Research proposal by T.Panov on toric topology for 2011-2013, supported by the grant of the Dynasty Foundation of 2010: English summary, proposal (in Russian)

• Toric topology in the work of T.Panov (2008) (pdf)
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