Finite-order algebraic automorphisms of affine varieties.
Finite-to-one restrictions of continuous functions
Finite-type invariants of Legendrian knots in the 3-space: Maslov index as an order 1 invariant
We consider a contractible closure of the space of Legendrian knots in the standard contact 3-space. We show that in this context the space of finite-type complex-valued invariants of Legendrian knots is isomorphic to that of framed knots in with an extra order 1 generator (Maslov index) added.
Finitude du nombre des classes d'isomorphisme des structures isométriques entières.
Finitude homotopique et isotopique des structures de contact tendues
Soit V une variété close de dimension 3. Dans cet article, on montre que les classes dhomotopie de champs de plans sur V qui contiennent des structures de contact tendues sont en nombre fini et que, si V est atoroïdale, les classes disotopie des structures de contact tendues sur V sont elles aussi en nombre fini.
Five dimensional Bieberbach groups with trivial centre.
Five-dimensional biquotients.
Fixed point data of finite groups acting on 3-manifolds.
Fixed point free equivariant homotopy classes
Fixed point free low dimensional real algebraic actions of A5 on contractible varieties.
Fixed point indices and manifolds with collars.
Fixed point indices of equivariant maps and Möbius inversions.
Fixed point sets of smooth group actions on disks and Euclidean spaces. A survey
Fixed point theory and the K-theoretic trace
The relationship between fixed point theory and K-theory is explained, both classical Nielsen theory (versus ) and 1-parameter fixed point theory (versus ). In particular, various zeta functions associated with suspension flows are shown to come in a natural way as “traces” of “torsions” of Whitehead and Reidemeister type.
Fixed point theory for homogeneous spaces, II
Let G be a compact connected Lie group, K a closed subgroup and M = G/K the homogeneous space of right cosets. Suppose that M is orientable. We show that for any selfmap f: M → M, L(f) = 0 ⇒ N(f) = 0 and L(f) ≠ 0 ⇒ N(f) = R(f) where L(f), N(f), and R(f) denote the Lefschetz, Nielsen, and Reidemeister numbers of f, respectively. In particular, this implies that the Lefschetz number is a complete invariant, i.e., L(f) = 0 iff f is deformable to be fixed point free. This was previously known under...
Fixed points and braids.
Fixed Points and Braids. II.
Fixed points and homotopy fixed points.
Fixed points for positive permutation braids
Making use of the Nielsen fixed point theory, we study a conjugacy invariant of braids, which we call the level index function. We present a simple algorithm for computing it for positive permutation cyclic braids.
Fixed points of actions of P-groups on projective varieties.