Algebraic properties of decorated splitting obstruction groups

A. Cavicchioli; Y. V. Muranov; D. Repovš

Bollettino dell'Unione Matematica Italiana (2001)

  • Volume: 4-B, Issue: 3, page 647-675
  • ISSN: 0392-4041

How to cite

top

Cavicchioli, A., Muranov, Y. V., and Repovš, D.. "Algebraic properties of decorated splitting obstruction groups." Bollettino dell'Unione Matematica Italiana 4-B.3 (2001): 647-675. <http://eudml.org/doc/196074>.

@article{Cavicchioli2001,
author = {Cavicchioli, A., Muranov, Y. V., Repovš, D.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {647-675},
publisher = {Unione Matematica Italiana},
title = {Algebraic properties of decorated splitting obstruction groups},
url = {http://eudml.org/doc/196074},
volume = {4-B},
year = {2001},
}

TY - JOUR
AU - Cavicchioli, A.
AU - Muranov, Y. V.
AU - Repovš, D.
TI - Algebraic properties of decorated splitting obstruction groups
JO - Bollettino dell'Unione Matematica Italiana
DA - 2001/10//
PB - Unione Matematica Italiana
VL - 4-B
IS - 3
SP - 647
EP - 675
LA - eng
UR - http://eudml.org/doc/196074
ER -

References

top
  1. AKHMET'EV, P. M., Splitting homotopy equivalences along a one-sided submanifold of codimension 1, Izv. Akad. Nauk SSSR Ser. Mat., 51 (2) (1987), 211-241 (in Russian); English transl. in Math. USSR Izv., 30 (2) (1988), 185-215. Zbl0643.57016
  2. AKHMET'EV, P. M.- MURANOV, YU. V., Obstructions to the splitting of manifolds with infinite fundamental group, Mat. Zametki, 60 (2) (1996), 163-175 (in Russian); English transl. in, Math. Notes, 60 (1-2) (1996), 121-129. Zbl0905.57020
  3. BROWDER, W.- LIVESAY, G. R., Fixed point free involutions on homotopy spheres, Bull. Amer. Math. Soc., 73 (1967), 242-245. Zbl0156.21903MR206965
  4. BUONCRISTIANO, S.- ROURKE, C. P.- SANDERSON, J., A Geometric Approach to Homology Theory, London Math. Soc. Lect. Note Ser., 18, Cambridge Univ. Press, Cambridge-New York-Melbourne, 1976. Zbl0315.55002MR413113
  5. CAPPELL, S. E.- SHANESON, J. L., Pseudo-free actions. I., in Algebraic Topology (Aarhus, 1978), Lect. Notes in Math., 763, Springer-Verlag, Berlin, 1979, 395-447. Zbl0416.57020MR561231
  6. CAVICCHIOLI, A.- HEGENBARTH, F., On 4-manifolds with free fundamental group, Forum Math., 6 (1994), 415-429. Zbl0822.57015MR1277705
  7. CAVICCHIOLI, A.- HEGENBARTH, F., A note on four-manifolds with free fundamental groups, J. Math. Sci. Univ. Tokyo, 4 (1997), 435-451. Zbl0893.57016MR1466355
  8. CAVICCHIOLI, A.- HEGENBARTH, F.- REPOVŠ, D., On the stable classification of certain 4-manifolds, Bull. Austral. Math. Soc., 52 (1995), 385-398. Zbl0863.57014MR1358695
  9. CAVICCHIOLI, A.- HEGENBARTH, F.- REPOVŠ, D., Four-manifolds with surface fundamental groups, Trans. Amer. Math. Soc., 349 (1997), 4007-4019. Zbl0887.57026MR1376542
  10. CAVICCHIOLI, A.- MURANOV, YU. V.- REPOVŠ, D., Spectral sequences in K -theory for a twisted quadratic extension, Yokohama Math. Journal, 46 (1998), 1-13. Zbl0958.19002MR1670761
  11. CAVICCHIOLI, A.- MURANOV, YU. V.- REPOVŠ, D., Una introduzione geometrica alla L-teoria, to appear. 
  12. R. K. DENNIS - C. PEDRINI - M. R. STEIN (Eds.), Algebraic K -Theory, Commutative Algebra, and Algebraic Geometry, Proceed. U.S.-Italy Joint Sem. (S. Margherita Ligure, June 18-24, 1989), Contemporary Math., 126Amer. Math. Soc.Providence, R.I., 1992. Zbl0742.00073MR1156497
  13. S. C. FERRY - A. A. RANICKI - J. ROSENBERG (Eds.), Novikov Conjectures, Index Theorems and Rigidity, Vol. 1, London Math. Soc. Lecture Notes, 226, Cambridge Univ. Press, Cambridge, 1995. Zbl0829.00027MR1388294
  14. FREEDMAN, M. H.- QUINN, F., Topology of 4-Manifolds, Princeton Univ. Press, Princeton, N. J., 1990. Zbl0705.57001MR1201584
  15. FREEDMAN, M. H.- TEICHNER, P., 4-Manifold topology I: Subexponential groups, Invent. Math., 122 (1995), 509-529. Zbl0857.57017MR1359602
  16. GRIGORCHUK, R. I., Degrees of growth of finitely generated groups and the theory of invariant means, Izv. Akad. Nauk. SSSR Ser. Mat., 48 (5) (1984), 939-985 (in Russian); English transl. in Math. USSR Izvestiya, 25 (1985), 259-300. Zbl0583.20023
  17. HAMBLETON, I., Projective surgery obstructions on closed manifolds, Algebraic K -theory, Part II (Oberwolfach 1980), Lect. Notes Math.967, Springer-Verlag, Berlin (1982), 101-131. Zbl0503.57018MR689390
  18. HAMBLETON, I.- KHARSHILADZE, A. F., A spectral sequence in surgery theory, Mat. Sb., 183 (9) (1992), 3-14 (in Russian); English transl. in, Russian Acad. Sci. Sb. Math., 77 (1994). Zbl0791.57022
  19. HAMBLETON, I.- MADSEN, I., On the computation of the projective surgery obstruction groups, K-theory, 7 (1993), 537-574. Zbl0797.57017MR1268592
  20. HAMBLETON, I.- MURANOV, YU. V., Projective splitting obstruction groups for onesided submanifolds, Mat. Sbornik, 190 (1999), to appear. Zbl0953.57017MR1740157
  21. HAMBLETON, I.- RANICKI, A.- TAYLOR, L., Round L -theory, J. Pure Appl. Algebra, 47 (1987), 131-154. Zbl0638.18003MR906966
  22. HAMBLETON, I.- TAYLOR, L.- WILLIAMS, B., An introduction to maps between surgery obstruction groups (1984), in Algebraic Topology (Aarhus, 1982), Lect. Notes in Math.1051, Springer-Verlag, Berlin-New York (1984), pp. 49-127. Zbl0556.57026MR764576
  23. HAMBLETON, I.- TAYLOR, L. R.- WILLIAMS, B., Detection theorems in K and L -theory, J. Pure Appl. Algebra, 63 (1990), 247-299. Zbl0718.18006MR1047584
  24. HILLMAN, J. A., The Algebraic Characterization of Geometric 4-Manifolds, London Math. Soc. Lect. Note Ser.198, Cambridge Univ. Press, Cambridge, 1994. Zbl0812.57001MR1275829
  25. KHARSHILADZE, A. F., The generalized Browder-Livesay invariant, Izv. Akad. Nauk. SSSR: Ser. Mat., 51 (2) (1987), 379-401 (in Russian); English transl. in: Math. USSR Izv., 30 (2) (1988), 353-374. Zbl0643.57017
  26. LOPEZ DE MEDRANO, S., Involutions on Manifolds, Springer-Verlag, Berlin-Heidelberg-New York, 1971. Zbl0214.22501MR298698
  27. MADSEN, I.- MILGRAM, R. J., The Classifying Spaces for Surgery and Cobordism of Manifolds, Ann. of Math. Studies92, Princeton Univ. Press, Princeton, N. J., 1979. Zbl0446.57002MR548575
  28. MURANOV, YU. V., Obstruction groups to splitting and quadratic extensions of antistructures, Izvestiya RAN: Ser. Mat., 59 (6) (1995), 107-132 (in Russian); English transl. in Izvestiya Math., 59 (6) (1995), 1207-1232. Zbl0996.57518
  29. MURANOV, YU. V., Relative Wall groups and decorations, Mat. Sbornik, 185 (12) (1994), 79-100 (in Russian); English transl. in, Russian Acad. Sci. Sb. Math., 83 (2) (1995), 495-514. Zbl0861.57043
  30. MURANOV, YU. V., Obstructions to surgeries of two-sheeted coverings, Mat. Sbornik, 131 (3) (1986), 347-356 (in Russian); English transl. in: Math. USSR Sbornik, 59 (2) (1998), 339-348. Zbl0624.57029
  31. MURANOV, YU. V., Splitting problem, Trudy MIRAN, 212 (1996), 123-146 (in Russian); English transl. in Proc. Steklov Inst. Math., 212 (1996), 115-137. Zbl0888.57029
  32. MURANOV, YU. V., Projective splitting obstruction groups and geometric antistructures, Abstracts of International Conference Dedicated to 90th Anniversary of L. S. Pontryagin. Geometry and Topology, Moscow, 1998. 
  33. MURANOV, YU. V.- KHARSHILADZE, A. F., Browder-Livesay groups of abelian 2-groups, Matem. Sbornik, 181 (8) (1990), 1061-1098 (in Russian); English transl. in Math. USSR Sb., 70 (1991). Zbl0732.55003
  34. MURANOV, YU. V.- REPOVŠ, D., Groups of obstructions to surgery and splitting for a manifold pair, Mat. Sb., 188 (3) (1997), 127-142 (in Russian); English transl. in Russian Acad. Sci. Sb. Math., 188 (3) (1997), 449-463. Zbl0881.57038
  35. MURANOV, YU. V.- REPOVŠ, D., Obstructions to reconstructions from a pair of manifolds, Uspehi Mat. Nauk., 51 (4) (1996), 165-166 (in Russian); English transl. in Russian Math. Surveys, 51 (4) (1996), 743-744. Zbl0881.57039
  36. NOVIKOV, S. P., Algebraic construction and properties of Hermitian analogs of K -theory over rings with involution from the viewpoint of Hamiltonian formalism. Applications to differential topology and theory of characteristic classes, I, II, Izv. Akad. Nauk SSSR. Ser. Mat., 34 (1970), 253-288 and 475-500 (in Russian); English transl. in Math. USSR Izv., 4 (1970), 257-292 and 479-505. Zbl0233.57009
  37. PEDRINI, C.- WEIBEL, C. A., K -theory and Chow groups on singular varieties, in Applications of Algebraic K-Theory to Algebraic Geometry and Number Theory I, II (Boulder, Colorado, 1983), Contemporary Math., 55Amer. Math. Soc., Providence, R.I. (1986), 339-370. Zbl0607.14002MR862641
  38. RANICKI, A. A., Exact Sequences in the Algebraic Theory of Surgery, Math. Notes26, Princeton Univ. Press, Princeton, N. J., 1981. Zbl0471.57012MR620795
  39. RANICKI, A. A., The L -theory of twisted quadratic extensions, Canad. J. Math., 39 (1987), 345-364. Zbl0635.57017MR899842
  40. RANICKI, A. A., Algebraic L -theory and Topological Manifolds, Cambridge Tracts in Mathematics, Cambridge University Press, 1992. Zbl0767.57002MR1211640
  41. RANICKI, A. A., High-dimensional knot theory, Math. Monograph, Springer-Verlag, Berlin-Heidelberg-New York, 1998. Zbl0910.57001MR1713074
  42. SWITZER, R., Algebraic Topology-Homotopy and Homology, Grund. Math. Wiss.212, Springer-Verlag, Berlin-Heidelberg-New York, 1975. Zbl0305.55001MR385836
  43. WALL, C. T. C., Surgery on Compact Manifolds, Academic Press, London - New York, 1970; Second Edition, A. A. Ranicki, Editor, Amer. Math. Soc., Providence, R. I., 1999. Zbl0219.57024
  44. WALL, C. T. C., On the axiomatic foundations of the theory of Hermitian forms, Proc. Cambridge Phil. Soc., 67 (1970), 243-250. Zbl0197.31103MR251054
  45. WALL, C. T. C., Foundations of Algebraic L -Theory, Proc. Conf. Battelle Memorial Inst. (Seattle, WA. 1972), Lect. Notes Math.343Springer-Verlag, Berlin, 1973. Zbl0269.18010MR357550
  46. WALL, C. T. C., Formulae for surgery obstructions, Topology, 25 (1976), 189-210. Zbl0338.57016MR423378
  47. WALL, C. T. C., Classification of Hermitian forms, VI. Group rings, Ann. of Math. (2), 103 (1976), 1-80. Zbl0328.18006MR432737

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.