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Mass endomorphism, surgery and perturbations

Bernd Ammann, Mattias Dahl, Andreas Hermann, Emmanuel Humbert (2014)

Annales de l’institut Fourier

We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.

Matrix factorizations and link homology

Mikhail Khovanov, Lev Rozansky (2008)

Fundamenta Mathematicae

For each positive integer n the HOMFLYPT polynomial of links specializes to a one-variable polynomial that can be recovered from the representation theory of quantum sl(n). For each such n we build a doubly-graded homology theory of links with this polynomial as the Euler characteristic. The core of our construction utilizes the theory of matrix factorizations, which provide a linear algebra description of maximal Cohen-Macaulay modules on isolated hypersurface singularities.

Maximal actions of finite 2-groups on ℤ₂-homology 3-spheres

Mattia Mecchia (2004)

Fundamenta Mathematicae

It is known that a finite 2-group acting on a ℤ₂-homology 3-sphere has at most ten conjugacy classes of involutions; the action of groups with the maximal number of conjugacy classes of involutions is strictly related to some questions concerning the representation of hyperbolic 3-manifolds as 2-fold branched coverings of knots. Using a low-dimensional approach we classify these maximal actions both from an algebraic and from a geometrical point of view.

Maximal Hamiltonian tori for polygon spaces

Jean-Claude Hausmann, Susan Tolman (2003)

Annales de l’institut Fourier

We study the poset of Hamiltonian tori for polygon spaces. We determine some maximal elements and give examples where maximal Hamiltonian tori are not all of the same dimension.

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