Cone complexes and PL 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].

Homotopy Types of Some Pl Complexes by Tadatoshi Akiba

Let PLn represent the semisimplicial group of germs of piecewise linear (PL), origin-preserving homeomorphisms of R. Since this is the structure group for ^-dimensional PL-bundles ([9], [8]), knowledge of its homotopy type is important for classifying PL structures. Beautiful work has been done in the stable range, making the intrinsic relations between differentiate, piecewise linear and topol...

Stability and Transversality

Generic Geometry, Transversality and Projections

In the paper [4] Montaldi proves a powerful transversality result which has a number of applications to the study of the generic geometry of submanifolds of Euclidean or projective space. As a typical application one can consider the contact of surfaces with spheres in Euclidean 3-space and describe the singularities that occur generically and, consequently, the local structure of the focal and...

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...