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A 2-category of chronological cobordisms and odd Khovanov homology

Krzysztof K. Putyra (2014)

Banach Center Publications

We create a framework for odd Khovanov homology in the spirit of Bar-Natan's construction for the ordinary Khovanov homology. Namely, we express the cube of resolutions of a link diagram as a diagram in a certain 2-category of chronological cobordisms and show that it is 2-commutative: the composition of 2-morphisms along any 3-dimensional subcube is trivial. This allows us to create a chain complex whose homotopy type modulo certain relations is a link invariant. Both the original and the odd Khovanov...

Algebraic equivalence of real algebraic cycles

Miguel Abánades, Wojciech Kucharz (1999)

Annales de l'institut Fourier

Given a compact nonsingular real algebraic variety we study the algebraic cohomology classes given by algebraic cycles algebraically equivalent to zero.

Bounded cohomology of lattices in higher rank Lie groups

Marc Burger, Nicolas Monod (1999)

Journal of the European Mathematical Society

We prove that the natural map H b 2 ( Γ ) H 2 ( Γ ) from bounded to usual cohomology is injective if Γ is an irreducible cocompact lattice in a higher rank Lie group. This result holds also for nontrivial unitary coefficients, and implies finiteness results for Γ : the stable commutator length vanishes and any C 1 –action on the circle is almost trivial. We introduce the continuous bounded cohomology of a locally compact group and prove our statements by relating H * b ( Γ ) to the continuous bounded cohomology of the ambient group...

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