topology@ub

Research Group in Algebraic Topology

Past Seminars

Homotopy types for Khovanov homology

    The aim of this seminar is to understand the Khovanov homotopy type constructed by Lipshitz and Sarkar in [4]. This is a space-level construction of Khovanov homology whose stable homotopy type is a well-defined invariant of the isotopy type of the link. The Khovanov homotopy type is a stronger invariant than Khovanov homology. For instance, its cohomology carries Steenrod operations, as shown in [6]. The construction of the spectra is inspired by a question posed by Cohen, Jones and Segal in [1] whether Floer homology equals the singular homology of some natural spectrum, and it is based on the concept of flow category. We will study Lipshitz and Sarkar's construction as well as some main properties and operations related to it.

    • Federico Cantero (UB) : Realisations of Khovanov spectra

      28 May 2018, 12:00, IMUB

    • Federico Cantero (UB): Further aspects of Khovanov homology

      14 May 2018, 12:00, IMUB

    • Marithania Silvero (UB): Extreme Khovanov spectra

      7 May 2018, 12:00, IMUB

    • Joana Cirici (UB): A Khovanov refinement following Hu-Kriz-Kriz

      26 April 2018, 14:30, IMUB
      Note that this week's session has been moved to THURSDAY.

    • Javier Gutiérrez (UB): Knot homology via cohomology of categories and homotopy limits II

      16 April 2018, 12:00, IMUB

    • Javier Gutiérrez (UB): Knot homology via cohomology of categories and homotopy limits

      9 April 2018, 12:00, IMUB

    • Carles Casacuberta (UB): Steenrod squares on Khovanov spectra

      12 March 2018, 12:00, IMUB

    • Federico Cantero (UB): Khovanov spectra after Lawson, Lipshitz and Sarkar

      We will give an exposition of some main ideas developed in [2] and [3].
      5 March 2018, 12:00, IMUB

    • Marithania Silvero (UB): A Khovanov homotopy type III

      26 February 2018, 12:00, IMUB

    • Marithania Silvero (UB): A Khovanov homotopy type II

      19 February 2018, 12:00, IMUB

    • Marithania Silvero (UB): A Khovanov homotopy type I

      12 February 2018, 12:00, IMUB

    References
    [1] R. L. Cohen, J. D. S. Jones and G. B. Segal, Floer's infinite-dimensional Morse theory and homotopy theory, The Floer Memorial Volume, 297-325, Progr. Math. 133, Birkhäuser, Basel, 1995.
    [2] T. Lawson, R. Lipshitz and S. Sarkar, Khovanov homotopy type, Burnside category and products, arXiv 1505.00213 (2015).
    [3] T. Lawson, R. Lipshitz and S. Sarkar, The cube and the Burnside category, arXiv 1505.00512 (2015).
    [4] R. Lipshitz and S. Sarkar, A Khovanov stable homotopy type, J. Amer. Math. Soc. 27 (2014), no. 4, 983-1042.
    [5] R. Lipshitz and S. Sarkar, A refinement of Rasmussen's s-invariant, Duke Math. J. 163 (2014), no. 5, 923-952.
    [6] R. Lipshitz and S. Sarkar, A Steenrod square on Khovanov homology, J. Topol. 7 (2014), no. 3, 817-848.