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Sergei V. Matveev

Sergei V. Matveev
http://ru.wikipedia.org/?oldid=88143252
Chelyabinsk State University, Chelyabinsk, Russian Federation

Faculty of Mathematics

Head of the Department of Computer Topology and Algebra

Academician of the Russian Academy of Sciences, PhD (Math.,Phys.), Professor

http://www.csu.ru/Lists/List4/sotrudnik.aspx?ID=83

http://www.ras.ru/win/db/show_per.asp?P=.id-237.ln-ru

ScopusID:  16407484100

ResearcherID:  J-5948-2013

ORCID ID:  0000-0001-6017-6006

 Scientific interests: Topology, Topology of Manifolds, Computer Topology

 Scientific achievements: A number of results have been obtained in the field of topology of manifolds, including the theory of elementary transformations of special polyhedra, the theory of complexity of three-dimensional manifolds, the equivalence of the Zeeman’s conjecture to the union of the Poincaré and Andrews-Curtis conjectures, the Zieschang problem, the hyperbolic three-dimensional manifold of the smallest volume (together with A.T. Fomenko).

The proof of the theorem on the algorithmic classification of three-dimensional manifolds, including the classification of classical knots, is completed. A theory of the roots of geometric objects was constructed, with the help of which theorems on primary decompositions for homologically trivial knots in thickened surfaces for virtual knots were proved, and a similar "folklore" theorem for orbifolds was disproved. Together with his students, he developed a theory of effective recognition of three-dimensional manifolds, constructed algorithms were implemented in the form of corresponding programs.

Main publications: 

  1. Matveev S.V. Algorithmic topology and classification of 3-manifolds. ACM-monographs, Second edition, Springer-Verlag Berlin Heidelberg, 2007. Vol. 9. 492 p. DOI: 10.1007/978-3-540-45899-9
  2. Matveev S.V. Lectures on Algebraic topology. European Mathematical Society, 2006, 108 p.
  3. Matveev, S.V. Roots and decompositions of three-dimensional topological objects // Russian Math. Surveys, 2012. Vol. 67, no. 3. P. 459–507. DOI: 10.1070/RM2012v067n03ABEH004794
  4. Matveev S.V. Prime decompositions of knots in T2×I // Topology and its Applications, 2012. Vol. 159. P. 1820–1824. DOI: 10.1016/j.topol.2011.04.022
  5. Matveev S.V. Tabulation of three-dimensional manifolds // Russian Math. Surveys, 2005. Vol. 60, no. 4. P. 673–698.
  6. Matveev S., Polyak M. Finite-type invariants of cubic complexes // Acta Applicandae Mathematica, 2003. Vol. 75, no. 1–3. P. 125–132. DOI: 10.1023/A:1022383927656
  7. Hayat-Legrand C., Matveev S.V. and Zieschang H. Computer calculation of the degree of maps into the Poincare homology sphere // Experimental Mathematics, 2001. Vol. 10, no. 4, P. 497–508. DOI: 10.1080/10586458.2001.10504669
  8. Matveev S.V. Complexity theory of three-dimensional manifolds // Acta Applicandae Mathematicae, 1990. Vol.19. P. 101–130. DOI: 10.1007/BF00049576
  9. Matveev S.V. Distributive groupoids in knot theory // Math. USSR-Sb., 1984. Vol. 47, no.1. P. 73–83. DOI: 10.1070/SM1984v047n01ABEH002630
  10. Matveev S.V. Special spines of piecewise linear manifolds // Math. USSR-Sb., 1973. Vol. 21, no. 2, P. 279–291. DOI: 10.1070%2FSM1973v021n02ABEH002017