Grey, Matthias On rational homological stability for block automorphisms of connected sums of products of spheres. (English) Zbl 1432.55024 Algebr. Geom. Topol. 19, No. 7, 3359-3407 (2019). This paper is concerned with the problem of understanding the rational homological structure of automorphism spaces of manifolds, similar in spirit to the highly connected even dimensional case considered by A. Berglund and I. Madsen [Pure Appl. Math. Q. 9, No. 1, 1–48 (2013; Zbl 1295.57038)]. The main theorems of this paper are homological stability results for the homotopy automorphisms and the block diffeomorphisms of connected sums of products of spheres. Reviewer: Abdelhadi Zaim (Casablanca) Cited in 3 Documents MSC: 55P62 Rational homotopy theory 57S05 Topological properties of groups of homeomorphisms or diffeomorphisms Keywords:classifying space; block diffeomorphisms; homological stability; homotopy automorphisms; manifolds; rational homology; rational homotopy theory Citations:Zbl 1295.57038 PDFBibTeX XMLCite \textit{M. Grey}, Algebr. Geom. Topol. 19, No. 7, 3359--3407 (2019; Zbl 1432.55024) Full Text: DOI arXiv References: [1] ; Bak, K-theory of forms. Annals of Mathematics Studies, 98 (1981) · Zbl 0465.10013 [2] 10.1007/BF02684586 · Zbl 0174.05203 · doi:10.1007/BF02684586 [3] 10.1090/S0002-9947-96-01555-3 · Zbl 0866.55007 · doi:10.1090/S0002-9947-96-01555-3 [4] 10.4310/PAMQ.2013.v9.n1.a1 · Zbl 1295.57038 · doi:10.4310/PAMQ.2013.v9.n1.a1 [5] 10.24033/asens.1269 · Zbl 0316.57026 · doi:10.24033/asens.1269 [6] 10.1007/978-1-4612-5987-9_2 · doi:10.1007/978-1-4612-5987-9_2 [7] 10.1016/0022-4049(87)90019-3 · Zbl 0615.20024 · doi:10.1016/0022-4049(87)90019-3 [8] 10.2140/agt.2003.3.1167 · Zbl 1063.18007 · doi:10.2140/agt.2003.3.1167 [9] 10.2307/1971200 · Zbl 0404.18012 · doi:10.2307/1971200 [10] 10.2307/1969702 · Zbl 0055.41704 · doi:10.2307/1969702 [11] 10.1007/s11511-014-0112-7 · Zbl 1377.55012 · doi:10.1007/s11511-014-0112-7 [12] 10.1090/jams/884 · Zbl 1395.57044 · doi:10.1090/jams/884 [13] 10.1007/BF01350084 · Zbl 0177.26101 · doi:10.1007/BF01350084 [14] 10.1007/BF01390018 · Zbl 0415.18012 · doi:10.1007/BF01390018 [15] 10.2307/1970128 · Zbl 0115.40505 · doi:10.2307/1970128 [16] ; Kirby, Foundational essays on topological manifolds, smoothings, and triangulations. Annals of Mathematics Studies, 88 (1977) · Zbl 0361.57004 [17] ; Kreck, Algebraic topology. Lecture Notes in Math., 763, 643 (1979) [18] 10.2307/1995262 · Zbl 0187.20304 · doi:10.2307/1995262 [19] 10.1007/978-3-642-30362-3 · Zbl 1260.18001 · doi:10.1007/978-3-642-30362-3 [20] 10.1016/j.jpaa.2006.05.019 · Zbl 1113.55007 · doi:10.1016/j.jpaa.2006.05.019 [21] 10.1090/tran/6564 · Zbl 1370.57010 · doi:10.1090/tran/6564 [22] 10.1112/jtopol/jtw004 · Zbl 1361.55012 · doi:10.1112/jtopol/jtw004 [23] 10.2307/1970725 · Zbl 0191.53702 · doi:10.2307/1970725 [24] ; Quinn, Topology of manifolds, 500 (1970) [25] 10.1093/qmath/20.1.255 · Zbl 0182.26201 · doi:10.1093/qmath/20.1.255 [26] 10.1215/ijm/1256065414 · doi:10.1215/ijm/1256065414 [27] 10.1007/BF01418871 · Zbl 0179.51803 · doi:10.1007/BF01418871 [28] 10.2307/1970425 · Zbl 0218.57022 · doi:10.2307/1970425 [29] 10.1016/0040-9383(63)90009-0 · Zbl 0123.16204 · doi:10.1016/0040-9383(63)90009-0 [30] 10.1515/9781400865215 · Zbl 0957.00062 · doi:10.1515/9781400865215 [31] 10.2307/1969506 · Zbl 0045.44202 · doi:10.2307/1969506 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.