A Fixed Point Index Theory for Symmetric Product Mappings.
A new invariant and parametric connected sum of embeddings
We define an isotopy invariant of embeddings of manifolds into Euclidean space. This invariant together with the α-invariant of Haefliger-Wu is complete in the dimension range where the α-invariant could be incomplete. We also define parametric connected sum of certain embeddings (analogous to surgery). This allows us to obtain new completeness results for the α-invariant and the following estimation of isotopy classes of embeddings. In the piecewise-linear category, for a (3n-2m+2)-connected...
On uncountable collections of continua and their span
We prove that if the Euclidean plane contains an uncountable collection of pairwise disjoint copies of a tree-like continuum X, then the symmetric span of X is zero, sX = 0. We also construct a modification of the Oversteegen-Tymchatyn example: for each ε > 0 there exists a tree such that σX < ε but X cannot be covered by any 1-chain. These are partial solutions of some well-known problems in continua theory.
Points multiples isolés d'immersions de codimension quatre.
Real cohomology groups of the space of nonsingular curves of degree 5 in