СПбГУ, мат-мех

 

 

 

 


English

Roman Mikhailov

 

 

 

E-mail

 

romanvm@mi.ras.ru

 

Research Interests 

 

Homotopy theory, group theory, homological and homotopical algebra

 

Publications and preprints

1. (with S. Melikhov) Links modulo knots and the problem of isotopic realization, Uspekhi Mat. Nauk 56 (2001), no. 2(338), 219--220;

2. Transfinite lower central series of groups: parafree properties and topological applications, Tr. Mat. Inst. Steklova 239 (2002), 251-267.

3. On invisible subgroups, Uspekhi Mat. Nauk 57 (2002), no. 6(348), 187--188.

4. (with I.B.S. Passi) Augmentation powers and group homology. J. Pure Appl. Algebra 192 (2004), no. 1-3, 225-238.

5. (with I.B.S. Passi) Higher traces on group rings. Comm. Algebra 33 (2005), no. 4, 987-997.

6. (with I.B.S. Passi) A transfinite filtration of Schur multiplicator. Internat. J. Algebra Comput. 15 (2005), no. 5-6, 1061-1073.

7. Residual nilpotence and residual solvability of groups, Sb. Math. 196 (2005), no. 11-12, 1659-1675.

8. On residual nilpotence of projective crossed modules. Comm. Algebra 34 (2006), no. 4, 1451-1458.

9. (with I.B.S. Passi) The quasi-variety of groups with trivial fourth dimension subgroup. J. Group Theory 9 (2006), no. 3, 369-381.

10. (with I.B.S. Passi) Faithfulness of certain modules and residual nilpotence of groups. Internat. J. Algebra Comput. 16 (2006), no. 3, 525-539.

11. Faithful group actions and aspherical complexes, Proc. Steklov Math. Inst. 252 (2006), 184-193.

12. (with V. Bardakov) On residual properties of some link groups, Sib. J. Math. 48 (2007) 485-495.

13. Baer invariants and residual nilpotence of groups, Izv. Mat. 71 (2007), 151-172.

14. (with I.B.S. Passi) Homology of centralizers, Comm. Alg. 35 (2007), 2191 - 2207.

15. Asphericity and residual properties of crossed modules, Sb. Mat. 198 (2007), 79-94.

16. (with I. Emmanouil) A limit approach to group homology, J. Algebra 319 (2008), 1450-1461, arXiv:0812.2092

17. (with V. Bardakov) On certain questions of the free group automorphism theory, Comm. Alg. 36 (2008), 1489-1499, arXiv:math/0701441

18. (with H.-J. Baues) Intersection of subgroups in free groups and homotopy groups, Internat. J. Algebra Comput, 18 (2008), 803-823, arXiv:0804.1999

19. (with I.B.S. Passi) Residually nilpotent groups, L'Enseignement Mathematique 54 (2008), 145-146.

20. (with I.B.S. Passi and M. Hartl) Dimension quotients, Journal of Indian Math. Soc (2009), 63-107; arXiv: 0803.3290

21. (with S. Melikhov) Quasi-isotopy III: Engel conditions,  arXiv: math.GT/0201022

22. (with H.-J. Baues) Homotopy types of reduced 2-nilpotent simplicial groups, Ind. J. Pure Appl. Math. 40 (2009), 35-80; arXiv:0804.2000

23. (with A. Belov) Free subalgebras of Lie algebras close to nilpotent, Groups, Geometry and Dynamics 4 (2010), 15-29; arXiv: 0805.0723

24. (with I.B.S. Passi) Limits over categories of extensions, Ind. J. Pure Appl. Math. 41 (2010), 113-131; arXiv: 0904.0634

25. (with G. Ellis) A colimit of classifying spaces, Advances in Math. 223 (2010), 2097-2113; arXiv:0804.3581

26. (with V. Bardakov, J. Wu, V.Vershinin) On the pure virtual braid group PV_3, Comm. Alg. 44 (2016), 1350-1378; arXiv: 0906.1743

27. (with V. Bardakov, J. Wu, V.Vershinin) Homotopy theory and group theory, Oberwolfach Reports, pdf (2008).

28. (with V. Bardakov,  J. Wu, V. Vershinin) Brunnian braids on surfaces, Alg. Geom. Top. 12 (2012) 1607-1648; arXiv: 0909.3387

29. (with J. Wu) On homotopy groups of the suspended classifying spaces, Alg. Geom. Top. 10 (2010), 565-625; arXiv: 0908.3580

30. (with L. Breen) Derived functors of non-additive functors and homotopy theory, Alg. Geom. Top. 11 (2011), 327-415; arXiv: 0910.2817

31. On the homology of the dual de Rham complexes, preprint; arxiv: 1001.2824

32. (with I.B.S. Passi and J. Wu) Symmetric ideals in group rings and simplicial homotopy, J. Pure Appl. Algebra 215 (2011), 1085-1092; arxiv: 1002.0128

33. (with J. Wu) Combinatorial group theory and the homotopy groups of finite complexes, Geom. Topol. (2013) 17, 235-273, arXiv: 1108.3055

34. (with J. Wu) Homotopy groups as centers of finitely presented groups, Izv. Mat. 77 (2013), 581-593  arXiv: 1108.6167

35. (with G. Baumslag and K. Orr) A new look at finitely generated metabelian groups, Contemporary Mathematics: Combinatorial and Computational Group Theory with Cryptography 582 (2012), 21-37; arXiv: 1203.5431

36. Polynomial functors and homotopy theory, Progress in Math, 311 (2016),  arXiv: 1202.0586

37. (with S.V. Ivanov ) On zero-divisors in group rings of groups with torsion, Canadian Math. Bull. 57 (2014), 326-334, arXiv: 1209.1443

38. Homotopical and combinatorial aspects of the theory of normal series in groups: a survey based on the Habil. Thesis, Proc. Steklov Math. Inst., 286, (2014), 1-135.  

39. Homotopy theory of Lie functors, (draft version): pdf (2012).

40. (with G. Baumslag) Residual properties of groups defined by basic commutators, Groups, Geometry and Dynamics 8 (2014), 621-642, http://arxiv.org/abs/1301.4629

41. (with G. Baumslag and K. Orr) Localization, metabelian groups and Isomorphism Problem, Trans. AMS, 369 (2017), 6823-6852, http://arxiv.org/abs/1301.5533 

42. (with K. Orr) Group localization and two problems of Levine, Math. Zeit. 280 (2015), 355-366, http://arxiv.org/abs/1306.6065

43. (with S.O. Ivanov) A higher limit approach to homology theories, J. Pure Appl. Algebra 219 (2015), 1915-1939, http://arxiv.org/abs/1309.4920

44. (with L. Breen and A. Touze) Derived functors of the divided power functors, Geom. Topol. 20 (2016), 257-352, http://arxiv.org/abs/1309.4920

45. A one-relator group with long lower central series, Forum Math. 28, (2016), 327-331, http://arxiv.org/abs/1406.2550

46. On transfinite nilpotence of the Vogel-Levine localization, Forum Math. 28, (2016), 333-338, http://arxiv.org/abs/1406.2554

47. (with S.O. Ivanov) On a problem of Bousfield for metabelian groups, Advances in Math 290 (2016), 552-589, http://arxiv.org/abc/1407.2959

48. (with S.O. Ivanov and J. Wu) Leibniz rule on higher pages of unstable spectral sequences, Proc. Edinburg Math. Soc. to appear, http://arxiv.org/abc/1503.08314

49. (with J. Wu) On the metastable homotopy of mod 2 Moore spaces, Alg. Geom. Top. 16 (2016), 1773-1797, http://arxiv.org/abc/1506.00945

50. (with F. Cohen and J.Wu) A combinatorial approach to the exponents of Moore spaces, Math. Z. to appear, http://arxiv.org/abc/1506.00948

51. (with S.O. Ivanov and J.Wu) On nontriviality of homotopy groups of spheres, HHA, 18 (2016), 337-344, http://arxiv.org/abc/1506.00952

52. (with I.B.S. Passi) Generalized dimension subgroups and derived functors, J. Pure Appl. Algebra 220 (2016), 2143-2163, http://arxiv.org/abc/150602124

53. (with S.O. Ivanov and J. Wu) Homotopy theory and generalized dimension subgroups, J. Algebra, 484 (2017), 224-246 http://arxiv.org/abs/1506.08324

54. (with I.B.S. Passi) The subgroup determined by a certain ideal in a free group ring, J. Algebra 449 (2016), 400-407, http://arxiv.org/abs/1508.04400

55. (with S. O. Ivanov) Higher limits, homology theories and fr-codes, http://arxiv.org/abs/1510.09044

56. (with I.B.S. Passi) Free group rings and derived functors, http://arxiv.org/abs/1605.08196

57. (with S. O. Ivanov) On lengths of HZ-localization towers, to appear Isr. J. of Math. http://arxiv.org/abs/1605.08198

58. (with I.B.S. Passi) Narain Gupta's three normal subgroup problem and group homology, http://arxiv.org/abs/1611.01313

59. (with I.B.S. Passi) Dimension quotients, Fox subgroups and limits of functors, http://arxiv.org/abs/1703.08304

60. (with E. Farjoun) On the third homotopy group of Orr's space, to appear Alg. Geom. Top., http://arxiv.org/abs/1703.10537

61. (with S. O. Ivanov) On discrete homology of a free pro-p-group, http://arxiv.org/abs/1705.09131

62. (with S. O. Ivanov) A finite Q-bad space, http://arxiv.org/abs/1708.00282

Book: (with I.B.S. Passi) Lower central and dimension series of groups, Lecture Notes in Mathematics 1952, Springer (2008), 354p.

 

Video lectures

 

Localization, completions and metabelian groups (2012) 

 http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=5762 

Derived functors in the sense of Dold-Puppe (in Russian) (2008) 

 http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=269 

Derived functors in the unstable homotopy theory (in Russian) (2010) 

 http://www.mathnet.ru/php/presentation.phtml?option_lang=rus&presentid=409 

 

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