Note on sequences of Mayer-Vietoris type
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- by Eldon Dyer and Joseph Roitberg PDF
- Proc. Amer. Math. Soc. 80 (1980), 660-662 Request permission
Abstract:
In this largely expository note, we reexamine the construction of the homotopical Mayer-Vietoris sequence associated to a homotopy pullback. We show that in this situation, the Mayer-Vietoris sequence may be realized simply as the homotopy sequence of a suitable fibration. The usual approaches to constructing the Mayer-Vietoris sequence involve some auxiliary algebraic result, such as the Barratt-Whitehead lemma; the present approach avoids any such considerations. An additional beneficial feature of our approach is the attention paid to the bottom end of the Mayer-Vietoris sequence. Thus we are led to a cleaner proof of Proposition II.7.11 of [HMR]; moreover, we show that the converse of this latter result is also true. The homological Mayer-Vietoris sequence associated to a homotopy pushout may be established in a very similar manner, as we point out at the end of the paper.References
- B. Eckmann and P. J. Hilton, Unions and intersections in homotopy theory, Comment. Math. Helv. 38 (1964), 293–307. MR 167982, DOI 10.1007/BF02566918
- Peter Hilton, Guido Mislin, and Joe Roitberg, Localization of nilpotent groups and spaces, North-Holland Mathematics Studies, No. 15, North-Holland Publishing Co., Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, 1975. MR 0478146
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 660-662
- MSC: Primary 55P99
- DOI: https://doi.org/10.1090/S0002-9939-1980-0587950-8
- MathSciNet review: 587950