I
am working in the area of Topology. My main research is concentrated in
the study of embedding spaces. I am using both the Vassiliev approach
of discriminants and the Goodwilllie-Weiss calculus method. My main
collaborators are Pascal Lambrechts, Greg Arone, Ismar Volic, and also
Dev Sinha, Paolo Salvatore, Ryan Budney. The study of these spaces is
fascinately related to the deformation theory (of operads) developped
by M. Kontsevich and Ya. Soibelman.
Thesis : "Sur les questions combinatoires de la theorie spectrale des noeuds" (pdf). Universite Paris 7, mai 2002. Thesis advisors : V.Vassiliev & P.Cartier.
Publications
[1] (Turchin) "Homology of Complexes of 2-Connected Graphs", Uspekhi Mat. Nauk 52 (1997), no.2, 189-190; English transl. in Russian Math. Surveys 52 (1997), no.2, 426-427.
[2] (Turchin) "Homology Isomorphism of the Complex of 2-Connected Graphs and the Graph-complex of Trees" (pdf) , AMS Transl. (2) Vol. 185, Advances in Mathematical Sciences Series 38 (1998), 147-153.
[3] (Turchin) "Spaces of Jets without Complicated Singularities" (pdf), Journal of Mathematical Science, Vol. 128 (4) 2005, pp. 3069-3087.
[4] (Tourtchine) "On the Homology of the Spaces of Long Knots", in "Advances in Topological Quantum Field Theory". NATO Sciences series by Kluwer 2005, pp 23-52. math. QA/0105140.
[5] (Turchin) "Computation of the first non-trivial 1-cocycle in the space of long knots", Mathem. Notes (Russia), Vol. 80 (1), pp 101-108. math. AT/0502518.
[6] (Tourtchine) "Dyer-Lashof-Cohen operations in Hochschild cohomology", Algebraic and Geometric Topology, Vol. 6, 2006, pp 875-894. math. RA/0504017.
[7] (Tourtchine) "What is one-term relation for higher homology of long knots", Moscow Math. J., Vol. 6 (1), April-Jume 2006, pp 169-194. math. AT/0510667.
[8] (Tourtchine) "On the other side of the bialgebra of chord diagrams", Journal of Knot Theory and its Ramifications, Vol. 16 (5), May 2007, pp 575-629. math. QA/0411436.
[9] P. Lambrechts, (Turchin) "Homotopy graph-complex for configuration and knot spaces", to appear in Trans. of AMS. math.AT/0611766.
[10] G. Arone, P. Lambrechts, (Turchin), I. Volic "Collapsing of the rational homotopy spectral sequence for the space of long knots in high codimension", to appear in Math. Res. Letters. math.AT/0701350
Preprints
[1] (Tourtchine) "Sur l'homologie des espaces de noeuds non-compacts", preprint IHES M/00/66, math. QA/0010017.
[2] P. Lambrechts, (Turchin), I. Volic "The map from the cyclohedron to the associahedron is left cofinal". Preprint IHES M/06/66, math.AT/0612591.
[3] P. Lambrechts, (Turchin), I. Volic "The rational homology of the space of long knots in codimension >2". math/0703649.
Thesis : "Sur les questions combinatoires de la theorie spectrale des noeuds" (pdf). Universite Paris 7, mai 2002. Thesis advisors : V.Vassiliev & P.Cartier.
Publications
[1] (Turchin) "Homology of Complexes of 2-Connected Graphs", Uspekhi Mat. Nauk 52 (1997), no.2, 189-190; English transl. in Russian Math. Surveys 52 (1997), no.2, 426-427.
[2] (Turchin) "Homology Isomorphism of the Complex of 2-Connected Graphs and the Graph-complex of Trees" (pdf) , AMS Transl. (2) Vol. 185, Advances in Mathematical Sciences Series 38 (1998), 147-153.
[3] (Turchin) "Spaces of Jets without Complicated Singularities" (pdf), Journal of Mathematical Science, Vol. 128 (4) 2005, pp. 3069-3087.
[4] (Tourtchine) "On the Homology of the Spaces of Long Knots", in "Advances in Topological Quantum Field Theory". NATO Sciences series by Kluwer 2005, pp 23-52. math. QA/0105140.
[5] (Turchin) "Computation of the first non-trivial 1-cocycle in the space of long knots", Mathem. Notes (Russia), Vol. 80 (1), pp 101-108. math. AT/0502518.
[6] (Tourtchine) "Dyer-Lashof-Cohen operations in Hochschild cohomology", Algebraic and Geometric Topology, Vol. 6, 2006, pp 875-894. math. RA/0504017.
[7] (Tourtchine) "What is one-term relation for higher homology of long knots", Moscow Math. J., Vol. 6 (1), April-Jume 2006, pp 169-194. math. AT/0510667.
[8] (Tourtchine) "On the other side of the bialgebra of chord diagrams", Journal of Knot Theory and its Ramifications, Vol. 16 (5), May 2007, pp 575-629. math. QA/0411436.
[9] P. Lambrechts, (Turchin) "Homotopy graph-complex for configuration and knot spaces", to appear in Trans. of AMS. math.AT/0611766.
[10] G. Arone, P. Lambrechts, (Turchin), I. Volic "Collapsing of the rational homotopy spectral sequence for the space of long knots in high codimension", to appear in Math. Res. Letters. math.AT/0701350
Preprints
[1] (Tourtchine) "Sur l'homologie des espaces de noeuds non-compacts", preprint IHES M/00/66, math. QA/0010017.
[2] P. Lambrechts, (Turchin), I. Volic "The map from the cyclohedron to the associahedron is left cofinal". Preprint IHES M/06/66, math.AT/0612591.
[3] P. Lambrechts, (Turchin), I. Volic "The rational homology of the space of long knots in codimension >2". math/0703649.