CURRICULUM VITAE
Born: 05. 09. 1956
Education:
1.
1973 - 1978 Faculty of Mechanics and Mathematics of Tbilisi State University.
2.
1978 - 1982 Post graduate student at A. Razmadze Mathematical
Institute of Georgian Academy of Sciences.
Degrees:
1.
1984 Candidate of Sciences (Ph.D.) at Tbilisi State University "On the
Axiomatic of Homology Theories ".
2.
1995 Doctor of Sciences (Habilitation) at Tbilisi State University
"Perturbation and Obstruction Theories in Fibre
Spaces".
Employment:
1982
- till now
employ of A. Razmadze Mathematical Institute,
Tbilisi:
1982
- 1995 -- Scientific researcher
1995
- 2006 -- Leader scientific researcher
2006
- 2017 -- Senior scientific researcher.
2017 - till now Principal
scientific researcher
Teaching
experiences:
1.
1980 - 1982 courses of Algebra at Tbilisi State University.
2.
1985 - 1989 courses of Algebraic Topology at Tbilisi State University.
3.
1992 - 1995 courses of Algebraic Topology at Tbilisi State University.
4.
2008 courses of
Algebraic Topology at Tbilisi State University.
Research
background and list of publications :
Algebraic
Topology: Homology and Homotopy
Theory of Fibrations, Algebraic Models of Topological
Spaces and Fibrations, Obstruction Theory.
Monographs:
1. Saneblidze, S., Perturbation and
obstruction theories in fibre spaces, Proc. A. Razmadze Math. Inst., 111, 1994, 1--106.
Papers:
1. Saneblidze, S., On the Steenrod
extraordinary homology theory, Bull. Acad. Sci. Georgian SSR (in Russian), 104 (1981), 281-284.
2. Saneblidze, S., On the uniqueness theorem
for the Steenrod-Sitnikov homology theory on the
category of compact Hausdorff spaces,
Bull. Acad. Sci.
Georgian SSR (in Russian), 105 (1982), 33-36.
3. Saneblidze, S., On the homology theory of paracompacta, Bull. Acad. Sci. Georgian SSR (in Russian), 109 (1983), 477-480.
4. Saneblidze, S., Extraordinary homology
theories of compact spaces, Proc. A. Razmadze Math.
Inst. (in Russian), 83 (1986), 88-101.
5. Saneblidze, S., On the uniqueness theorem
for the homology theory of paracompacta, Proc. A. Razmadze Math. Inst. (in Russian), 97 (1992), 53-64.
6. Saneblidze, S., Functor Dk and
rational cohomology algebra of a fiber space, Bull.Acad. Sci. Georgian SSR (in Russian), 128 (1987),
261-264.
7. Saneblidze, S., Functor D and rational cohomology of a fiber space, Bull. Acad. Sci. Georgian SSR
(in Russian), 129 (1988), 17-19.
8. Saneblidze, S., Homology classification of
differential algebras, Bull. Acad. Sci. Georgian SSR (in Russian), 129 (1988), 241-243.
9. Saneblidze, S., Obstruction theory in
rational homotopy theory, Bull. Acad. Sci. Georgian SSR (in
Russian), 134 (1989), 53-55.
10.
Saneblidze, S., Hopf filtered model in rational homotopy theory, Bull. Acad. Sci. Georgian SSR, 136 (1989), 545-547.
11.
Saneblidze, S., On the rational cuplength of certain
path spaces, Preprint of A. Razmadze Math. Inst. (1991),
1-7.
12.
Saneblidze, S., The set of multiplicative predifferentials
and the rational cohomology algebra of fibre spaces, J. of Pure and Appl. Algebra, 73 (1991),
277-306.
13.
Saneblidze, S., Filtered model of a fibration and
rational obstruction theory, Manuscripta Math., 76
(1992), 111-136.
14.
Saneblidze, S., Obstructions to the section problem in fibre
bundles, Manuscripta Math., 81 (1993), 95-111.
15.
Saneblidze, S., On the homotopy classification of
sections in the free loop fibration, J. of Pure and Appl.
Algebra, 91 (1994), 317-327.
16.
Saneblidze, S., Lusternik-Schnirelmann category of a
weak formal space, Bull. Georgian Acad. Sci., 154 (1996), 351-352.
17.
Saneblidze, S. et all, On the Obstruction functor, Bull. Georgian Acad. Sci.,
153 (1996), 130-136.
18.
Saneblidze, S., Obstructions in a fibration with a
weak formal base. Bull. Georgian Acad. Sci., 153 (1996), 199-202.
19.
Saneblidze, S., On a multiplicative model of a fibration
(with T. Kadeishvili), Bull. Georgian Acad. Sci., 153
(1996), 345-346.
20.
Saneblidze, S., Iterating the bar construction (with T. Kadeishvili),
Bull. Georgian Acad. Sci., 154 (1996), 338-340.
21.
Saneblidze, S., The formula determining an A∞-coalgebra
structure on a free algebra, Bull. Georgian Acad. Sci., 154 (1996), 351-352.
22.
Saneblidze, S., Obstructions to the section problem in a fibration
with a weak formal base,
Georgian Math. J., 4 (1997), 149-162.
23.
Saneblidze, S., Homotopy classification of spaces
with fixed Pontrjagin algebra, Bull. Georgian Acad.
Sci., 157 (1998), 11-13.
24.
Saneblidze, S., Functor D with coefficients in an extraordinary homology
theory, Bull. Georgian Acad. Sci., 158 (1998), 211-213.
25.
Saneblidze, S. (with T. Kadeishvili), The cobar construction as a cubical complex, Bull. Georgian
Acad. Sci., 158 (1998), 17-19.
26.
Saneblidze, S. (with T. Kadeishvili), Iterating the
bar construction, Georgian Math. J., 5 (1998), 441-452.
27.
Saneblidze, S. (with T. Kadeishvili), Permutohedral
complex model for the double loop space, Proc. of the International Meeting,
ISPM-98,
Mathematical
Methods in Modern Theoretical Physics, School and Workshop, Tbilisi, Georgia,
September 5-18 (1998), 231-236.
28.
Saneblidze, S., On the homotopy classification of
spaces by the fixed loop space homology, Proc. A. Razmadze
Math. Inst., 119 (1999), 155-164.
29.
Saneblidze, S. (with R. Umble), Diagonals on the permutahedra, multiplihedra and associahedra, J. Homotopy,
Homology and Appl., 6(1), (2004), 363-411.
30.
Saneblidze, S. (with T. Kadeishvili), A cubical model
of a fibration, J. Pure and Appl. Algebra, 196
(2005), 203-228.
31.
Saneblidze, S. (with R. Umble), The biderivative and A∞-bialgebras,
J. Homology, Homotopy and Appl., 7(2) (2005),
161-177.
32.
Saneblidze, S., On derived categories and derived functors, Extracta Mathematicae, 22
(2007), 315-324.
33.
Saneblidze, S., The bitwisted Cartesian model for the
free loop fibration, Topology and its Appl., 156
(2009), 897-910.
34.
Saneblidze, S., On the homotopy classification of maps, J. of homotopy and related struct., 4 (2009), 347-357.
35.
Saneblidze, S., On the Betti numbers of a loop space, J. of homotopy and related struct., 5(1), (2010),
1-13.
36.
Saneblidze, S. (with R. Umble), Matrads, biassociahedra and A∞-bialgebras, J. Homology, Homotopy
and Appl., 13(1), (2011), 1-57 .
37.
Saneblidze, S. (with T. Kadeishvili), The twisted Cartesian model for the
double path space fibration, Georgian Math. J., 22
(4) (2015), 489-508.
38.
Saneblidze, S., Filtered Hirsch algebras, Trans. R.M.I., 170 (2016), 114-136.
39.
Saneblidze, S., The loop cohomology of a space with
the polynomial cohomology algebra, Trans. R.M.I., 171 (2017),
389--395.
40.
Saneblidze, S. (with M. Rivera), A combinatorial model for the path fibration, JHRS, 14 (2019), 393--410.
41.
Saneblidze, S. (with M. Rivera), A combinatorial model for the free loop fibration, Bull. L.M.S., 50 (2018), 1085--1101.
42. Saneblidze, S. On the construction of a
covering map, Georgian Math. J., 26 (2) (2019), 303--310.
43.
Saneblidze, S. Intersection and string
topology products in the free
loop fibration, Trans. R.M.I.,
173(2)(2019), 161--164.
44.
Saneblidze, S. On the secondary cohomology operations, Trans. R.M.I., 174(3) (2020), 429--433.
45.Saneblidze,
S. (with R.Umble), Framed Matrices and $A_{\infty}$-Bialgebras, ASETMJ, 15(4) (2022), 41--140.
46.
Saneblidze, S. (with R.Umble), Comparing Diagonals on the Associahedra, Homology, Homotopy
and Appl., 26(1) (2024), 141--149.
Preprints:
1.
Saneblidze, S. (with R. Umble),
A diagonal of associahedra, preprint,
math. AT/0011065.
2. Saneblidze, S., On the
homology theory of the closed geodesic problem, preprint, math. AT/1106.5090.
3. Saneblidze, S., On the L∞-bialgebra structure of the ratonal homotopy groups π∗(ΩΣY)⊗Q, preprint,
math.AT/2311.15256.