Coordinate morse theory.
Co-rank and Betti number of a group
For a finitely generated group, we study the relations between its rank, the maximal rank of its free quotient, called co-rank (inner rank, cut number), and the maximal rank of its free abelian quotient, called the Betti number. We show that any combination of the group's rank, co-rank, and Betti number within obvious constraints is realized for some finitely presented group (for Betti number equal to rank, the group can be chosen torsion-free). In addition, we show that the Betti number is additive...
Corners and Arithmetic Groups
Corollaries of the A-H-V formula.
Correction for the paper “-bundles and exotic actions”
In [R] explicit representatives for -principal bundles over are constructed, based on these constructions explicit free -actions on the total spaces are described, with quotients exotic -spheres. To describe these actions a classification formula for the bundles is used. This formula is not correct. In Theorem 1 below, we correct the classification formula and in Theorem 2 we exhibit the correct indices of the exotic -spheres that occur as quotients of the free -actions described above.
Correction to: "An obstruction to smoothing of Gorenstein surface singularities".
Correction to "Constructing Lens Spaces by Surgery on Knots".
Correction to "Locally flat 2-spheres in simply connected 4-manifolds".
Correction to “Open books and configurations of symplectic surfaces”.
Correction to “Properties of pseudoholomorphic curves in symplectisations. I : asymptotics”
Correction to: SK1 for Finite Group Rings: I.
Correction to the paper “Compact fiberings of homogeneous spaces. I”
Correspondence between diffeomorphism groups and singular foliations
It is well-known that any isotopically connected diffeomorphism group G of a manifold determines a unique singular foliation . A one-to-one correspondence between the class of singular foliations and a subclass of diffeomorphism groups is established. As an illustration of this correspondence it is shown that the commutator subgroup [G,G] of an isotopically connected, factorizable and non-fixing diffeomorphism group G is simple iff the foliation defined by [G,G] admits no proper minimal sets....
Correspondence between maximal ideals in associative algebras and Lie algebras
Corrigendum et addendum ad: “Minimal cell coverings of sphere bundles over spheres”
Corrigendum to: "Aspherical four-manifolds and the centres of two-knot groups".
Corrigendum to Resolutions of homology manifolds, and the topological characterization of manifolds.
Counterexamples to representing homology classes by real algebraic subvarieties up to homeomorphism
Counterexamples to the Kneser conjecture in dimension four.
Counting fixed points of a finitely generated subgroup of Aff [C].
Given a finitely generated subgroup G of the group of affine transformations acting on the complex line C, we are interested in the quotient Fix( G)/G. The purpose of this note is to establish when this quotient is finite and in this case its cardinality. We give an application to the qualitative study of polynomial planar vector fields at a neighborhood of a nilpotent singular point.