On tangential transversality

Alexander Invariants and Transversality

We show that some of the main results in Laurentiu Maxim’s paper [10] can be obtained (even in a slightly more general setting) using the theory of perverse sheaves of finite rank over Q as described for instance in author’s recent book [3].

Transversality in Generalized Manifolds

Suppose that X is a generalized n-manifold, n 5, satisfying the disjoint disks property, and M and Q are topologicalmand q-manifolds, respectively, 1-LCC embedded in X, with n m 3 and n q 3. We de ne what it means for M to be stably transverse to Q in X. In the metastable range, 3m 2(n 1) and 3(m+ q) < 4(n 1), we show that there is an arbitrarily small homotopy of M to a 1-LCC embedding that is...

Symmetry Reduction without Transversality

We present a generalization of Lie’s method for finding the group invariant solutions to a system of partial differential equations. Our generalization relaxes the standard transversality assumption and encompasses the common situation where the reduced differential equations for the group invariant solutions involve both fewer dependent and independent variables. The theoretical basis for our ...

Transversality for Z2-orbifolds

Equivariant transversality phenomena are studied for PL locally linear actions of the group with two elements. In this setting with stability assumptions, the obstruction to making a given map f : M ! N transverse to the xed set N Z 2 is given by an element of Sect(BL(M ; N) # M Z 2), i.e. a generalized cohomology class with twisted coeecients. Here BL(M ; N) is a spectrum whose homotopy groups...

Stability and Transversality