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English
Михайлов Роман Валерьевич

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Research Interests

Publications and preprints

Books

Video lectures

E-mail

 romanvm@mi.ras.ru

 

Research Interests 

 Homotopy theory, group theory, homological and homotopical algebra

 

Publications and preprints 


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

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

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

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

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

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

51. (with S.O. Ivanov and J.Wu) On nontriviality of homotopy groups of spheres, HHA, to appear, http://arxiv.org/abc/1506.00952

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

49. (with J. Wu) On the metastable homotopy of mod 2 Moore spaces, Alg. Geom. Top. to appear, http://arxiv.org/abc/1506.00945

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

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

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

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

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

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

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

41. (with G. Baumslag and K. Orr) Localization, metabelian groups and Isomorphism Problem, Trans. AMS, to appear, http://arxiv.org/abs/1301.5533 

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

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

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.  

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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.

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

7. Residual nilpotence and residual solvability of groups. Mat. Sb. 196 (2005), no. 11, 109-126; translation in Sb. Math. 196 (2005), no. 11-12, 1659-1675.

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

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

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

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

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

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

 

Books 

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

 

Video lectures 

3. Localization, completions and metabelian groups (2012) 

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

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

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

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

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

 

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