Research Group in Algebraic Topology

Tame Homotopy Theory and Transformation Groups

The objective of the seminar will be to understand Hanke's work [Han09]. Along the way we will study general applications of rational homotopy to the theory of transformation groups, and its extension to tame homotopy theory, which deals with Fp-coefficients. There will be a few preliminary sessions on the theory of transformation groups and on rational homotopy before we move on to reading Hanke's paper.

  • Joana Cirici: Introduction

    6 February 2023, 12:00, IMUB

    [ Notes ]

  • Jordi Daura: Borel construction, equivariant cohomology, Mann-Su Theorem

    13 February 2023, 12:00, IMUB

    [ Notes ]

  • Ignasi Mundet: General considerations on transformation group theory

    20 February 2023, 12:00, IMUB

  • Roger Garrido: Rational homotopy theory, model of the Borel fibration

    27 February 2023, 12:00, IMUB

    [ Notes ]

  • Joana Cirici: Finite-dimensional rational homotopy

    6 March 2023, 12:00, IMUB

  • Sergio García: Proof of the main theorem of [Han09]

    13 March 2023, 12:00, IMUB

  • Jordi Garriga: The Cenkl-Porter complex

    20 March 2023, 12:00, IMUB

    [ Notes ]

  • Anna Sopena-Gilboy: Tame homotopy theory

    27 March 2023, 12:00, IMUB

  • Pedro Magalhaes: Tame Hirsch Lemma

    17 April 2023, 12:00, IMUB

  • Ignasi Mundet: Tame equivariant minimal models

    24 April 2023, 12:00, IMUB

  • Jordi Daura: Tame equivariant minimal models II

    8 May 2023, 12:00, IMUB

  • Joana Cirici: Loose ends and perspectives

    15 May 2023, 12:00, IMUB

[AP93] C. Allday and V. Puppe, Cohomological methods in transformation groups, Cambridge Studies in Advanced Mathematics, vol. 32, Cambridge University Press, Cambridge (1993).
[CP84] B. Cenkl and R. Porter, De Rham theorem with cubical forms, Pacific J. Math. (1984).
[Hal77] S. Halperin, Finiteness in the minimal models of Sullivan, Trans. Amer. Math. Soc. (1977).
[Han09] B. Hanke, The stable free rank of symmetry of products of spheres, Invent. Math. (2009).

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