• Differentiable Structures on Spheres and the Kervaire Invariant 

      Haus, Knut Bjarte (Master thesis, 2017)
      We follow Kervaire Milnor in defining and studying the group G of smooth structures on the sphere S^n. Surgery theory is developed and applied to study the subgroup bP^(n+1) of G. The Pontryagin construction induces a ...
    • Geometric Hodge filtered complex cobordism 

      Haus, Knut Bjarte (Doctoral theses at NTNU;2022:238, Doctoral thesis, 2022)
      We define geometric Hodge filtered complex cobordism groups MUn(p)(X) for complex manifolds X. Refining the Pontryagin–Thom construction, we give a natural isomorphism MUn(p)(X) ƒ MUnD (p)(X), where MUnD(p)(X) are the Hodge ...
    • Geometric Hodge filtered complex cobordism 

      Haus, Knut Bjarte; Quick, Gereon (Peer reviewed; Journal article, 2023)
      We construct a geometric cycle model for a Hodge filtered extension of complex cobordism for every smooth manifold with a filtration on its de Rham complex with complex coefficients. Using a refinement of the Pontryagin–Thom ...