The block structure spaces of real projective spaces and orthogonal calculus of functors

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dc.creatorMacko, Tibor
dc.date2004-04-09
dc.date2007-03-13
dc.date.accessioned2026-07-07T07:51:21Z
dc.date.available2026-07-07T07:51:21Z
dc.descriptionGiven a compact manifold X, the set of simple manifold structures on X x Δ^k relative to the boundary can be viewed as the k-th homotopy group of a space §^s (X). This space is called the block structure space of X. We study the block structure spaces of real projective spaces. Generalizing Wall's join construction we show that there is a functor from the category of finite dimensional real vector spaces with inner product to the category of pointed spaces which sends the vector space V to the block structure space of the projective space of V. We study this functor from the point of view of orthogonal calculus of functors; we show that it is polynomial of degree <= 1 in the sense of orthogonal calculus. This result suggests an attractive description of the block structure space of the infinite dimensional real projective space via the Taylor tower of orthogonal calculus. This space is defined as a colimit of block structure spaces of projective spaces of finite-dimensional real vector spaces and is closely related to some automorphisms spaces of real projective spaces.
dc.descriptioncorrected version, 32 pages, published in Transactions of the AMS at http://www.ams.org/tran/2007-359-01/S0002-9947-06-04180-8/
dc.identifierhttps://arxiv.org/abs/math/0404198
dc.identifierhttp://arxiv.org/abs/math/0404198
dc.identifierTransactions of the American Mathematical Society, Volume 359, Number 1, January 2007, pages 349-383
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/125481
dc.subjectAlgebraic Topology
dc.subjectPrimary: 57N99, 57P99; Secondary: 57R67
dc.titleThe block structure spaces of real projective spaces and orthogonal calculus of functors
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