Tore August Kro

• Baas, Nils Andreas; Bökstedt, Marcel & Kro, Tore August (2012). Two-Categorical Bundles and their Classifying Spaces. Journal of K-Theory. ISSN 1865-2433. 10(2), s. 299–369. doi: 10.1017/is012001012jkt181.
• Kro, Tore August (2007). Model structure on operads in orthogonal spectra. Homology, Homotopy and Applications. ISSN 1532-0073. 9(2), s. 397–412. Vis sammendrag

  We generalize Berger and Moerdijk's results on axiomatic homotopy theory for operads to the setting of enriched symmetric monoidal model categories, and show how this theory applies to orthogonal spectra. In particular, we provide a symmetric fibrant replacement functor for the positive stable model structure.

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• Gulbrandsen, Martin G; Kleppe, Johannes; Kro, Tore August & Vatne, Jon Eivind (2015). Matematikk for ingeniørfag - oppgaver og fasit. Gyldendal Norsk Forlag A/S. ISBN 9788205477964. 288 s.
• Gulbrandsen, Martin G; Kleppe, Johannes; Kro, Tore August & Vatne, Jon Eivind (2013). Matematikk for ingeniørfag. Gyldendal Akademisk. ISBN 9788205432338. 720 s.

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• Kro, Tore August (2016). A Whitney embedding theorem for a class of stratified Frölicher spaces and thoughts about Thom's isotopy lemmas.
• Kro, Tore August (2016). A Whitney embedding theorem for a class of stratified Frölicher spaces and thoughts about Thom's isotopy lemmas.
• Kro, Tore August (2013). Topologi og data.
• Gulbrandsen, Martin G; Kleppe, Johannes; Kro, Tore August & Vatne, Jon Eivind (2013). Digital arbeidsbok til Matematikk for ingeniørfag.
• Kro, Tore August (2013). A category of stratified spaces. Vis sammendrag

  Can we find a category of stratified spaces such that embeddings into Euclidean space has images satisfying Whitneys conditions A and B? Thom and Mathers intrinsic definitions are overloaded with data on how the pieces fit along corners. In 1967 Boman proves that a function $f$ in several variables is smooth if and only if the composition with any smooth curve $c$ gives a smooth function $f\circ c$ in one variable. Frölicher has axiomatized this result creating a category of spaces with smooth structure. Unlike the category of manifolds and smooth maps, this new category has all limits and colimits. Using the half open interval $[0,1>$ and certain push-out diagrams I construct a class of Frölicher spaces that resemble Whitney stratified sets. For any such space $W$ we consider smooth maps into Euclidean space of high dimension. Employing mainly Hadamards lemma, we will analyze the geometry of the tangent spaces across strata.

• Kro, Tore August (2013). Intervju om Pi på Pi-dagen. [Radio]. NRK Østfold.
• Kro, Tore August (2011). Pi er feil.
• Kro, Tore August (2011). 2-Manifold bundles.
• Blom, Hans Andreas; Hauge, Bjørn Gitle & Kro, Tore August (2009). Prosjektet "Realfagsatsing i regionen" : hva har skjedd til nå?
• Kro, Tore August (2009). Principal Two-Bundles and Manifoldbundles. Vis sammendrag

  Et simplisielt rom kan betraktes som tillatte transisjonsdata for en klasse bunter. I dette seminaret spesialiserer vi til geometriske nerver av topologiske 2-kategorier og får prinsipale 2-bunter. I tillegg spekulerer vi på bunter der transisjonsdataene over n-fold snitt er gitt ved (n-1)ste ordens kobordismer.

• Kro, Tore August (2009). Stratified Spaces. Vis sammendrag

  We will construct certain stratified spaces inside the category of F rölicher spaces. Various ways of generalizing the notion of tangent space for a manifold will be discussed. For different purposes all o f the following seem relevant: Flow spaces, curve spaces, ray spaces and continuous derivations. The differences between these will be i lluminated by basic examples. We will introduce type A and type B em beddings and prove that the image of a locally compact sharp stratif ied space under a type B embedding into an Euclidean space naturally gets the structure of a Whitney stratified set. Furthermore, I will indicate an approach to Thom's first isotopy lemma.

• Kro, Tore August (2009). Stratified Spaces. Vis sammendrag

  We will construct certain stratified spaces inside the category of F rölicher spaces. Various ways of generalizing the notion of tangent space for a manifold will be discussed. For different purposes all o f the following seem relevant: Flow spaces, curve spaces, ray spaces and continuous derivations. The differences between these will be i lluminated by basic examples. We will introduce type A and type B em beddings and prove that the image of a locally compact sharp stratif ied space under a type B embedding into an Euclidean space naturally gets the structure of a Whitney stratified set. Furthermore, I will indicate an approach to Thom's first isotopy lemma.

• Kro, Tore August (2008). Two-categorical bundles and their classifying spaces. Vis sammendrag

  For a 2-category 2C we associate a notion of a principal 2C-bundle. In case of the 2-category of 2-vector spaces in the sense of M.M. Kapranov and V.A. Voevodsky this gives the the 2-vector bundles of N.A. Baas, B.I. Dundas and J. Rognes. Our main result says that the geometric nerve of a good 2-category is a classifying space for the associated principal 2-bundles. In the process of proving this we develop a lot of powerful machinery which may be useful in further studies of 2-categorical topology. As a corollary we get a new proof of the classification of principal bundles. A calculation based on the main theorem shows that the principal 2-bundles associated to the 2-category of 2-vector spaces in the sense of J.C. Baez and A.S. Crans split, up to concordance, as two copies of ordinary vector bundles.

• Baas, Nils Andreas; Bøhstedt, Marcel & Kro, Tore August (2006). 2-categorical K-theories. Norwegian University of Science and Technology, Trondheim Norway.

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