Floppy Curves with Applications to Real Algebraic Curves

We show how one may sometimes perform singular ambient surgery on the complex locus of a real algebraic curve and obtain what we call a floppy curve. A floppy curve is a certain kind of singular surface in CP(2), more general than the complex locus of a real nodal curve. We derive analogs for floppy curves of known restrictions on real nodal curves. In particular we derive analogs of Fielder's congruence for certain nonsingular curves and Viro's inequalities for nodal curves which generalize those of Arnold and Petrovskii for nonsingular curves. We also obtain a determinant condition for certain curves which are extremal with respect to some of these equalities. One may prohibit certain schemes for real algebraic curves by prohibiting the floppy curves which result from singular ambient surgery. In this way, we give a new proof of Shustin's prohibition of the scheme $1>$ for a real algebraic curve of degree eight.Comment: AmS-TeX- Version 2.1, 38 pages with 16 figures,needs epsf.tex The estimate 9.6 has been improved with corresponding changes in 4.1. The exposition in the proof of 3.4 has been improved. Other minor change

On the Frohman Kania-Bartoszynska ideal

The Frohman Kania-Bartoszynska ideal is an invariant associated to a 3-manifold with boundary and a prime p >3. We give some estimates of this ideal. We also calculate this invariant for some 3-manifolds constructed by doing surgery on a knot in the complement of another knot.Comment: 7pages, 1 figur

Restoring Trust: The Role of HR in Corporate Governance

Theories of knowledge-based competition focus on internal resources as the source of value creation. The HR architecture (Lepak & Snell, 1999) brought human resource management directly into this forum by developing a model of human capital allocation and management. We attempt to extend the HR architecture by introducing a framework of relational archetypes—entrepreneurial and cooperative—that are derived from unique combinations of three dimensions (cognitive, structural, and affective) that characterize internal and external relationships of core knowledge employees. Entrepreneurial archetypes facilitate value creation from external partnerships while cooperative archetypes facilitate value creation from internal partnerships. This paper identifies how each of these archetypes is managed by a corresponding HR configuration and how they together contribute to value creation by facilitating organizational learning via exploration and exploitation

Skein theory and Witten-Reshetikhin-Turaev Invariants of links in lens spaces

We study the behavior of the Witten-Reshetikhin-Turaev SU(2) invariants of links in L(p,q) as a function of the level r-2. They are given by 1 over the square root of r times one of p Laurent polynomials evaluated at e to the 2 pi i divided by 4pr. The congruence class of r modulo p determines which polynomial is applicable. If p is zero modulo four, the meridian of L(p,q) is non-trivial in the skein module but has trivial Witten-Reshetikhin-Turaev SU(2) invariants. On the other hand, we show that one may recover the element in the Kauffman bracket skein module of L(p,q) represented by a link from the collection of the WRT invariants at all levels if p is a prime or twice an odd prime. By a more delicate argument, this is also shown to be true for p=9.Comment: Much of the paper has been rewritten and simplified. The only if part of theorem 2 is new. AMS-TeX, 10 page

Two functions on Sp(g,R)

We consider two functions on Sp(g,R) with values in the cyclic group of order four {1,-1,i,-i}. One was defined by Lion and Vergne. The other is -i raised to the power given by an integer valued function defined by Masbaum and the author (initially on the mapping class group of a surface). We identify these functions when restricted to Sp(g,Z). We conjecture the identity of these functions on Sp(g,R).Comment: 8 page

Quantum invariants of periodic three-manifolds

Let p be an odd prime and r be relatively prime to p. Let G be a finite p-group. Suppose an oriented 3-manifold M-tilde has a free G-action with orbit space M. We consider certain Witten-Reshetikhin-Turaev SU(2) invariants w_r(M). We will give a fomula for w_r(M) in terms of the defect of M-tilde --> M and the number of elements in G. We also give a version of this result if M and M-tilde contain framed links or colored fat graphs. We give similar formulas for non-free actions which hold for a specified finite set of values for r.Comment: 19 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon2/paper9.abs.htm

The Doctrine of Collateral Estoppel in Parole Revocation

In recent years courts have shown more recognition of the rights of parolees and probationers. Spurred by a Supreme Court decision that certain due process protections were applicable to parole revocation procedures, revocation hearings are now providing parolees and probationers some of the procedural protections available to criminal defendants at trial. Policy considerations have dictated, however, that the protections available at revocation hearings must fall far short of conferring upon the accused the full panoply of rights due a defendant at trial. As a result of the Supreme Court\u27s emphasis on the difference between revocation hearings and criminal proceedings, lower courts have held that some constitutional protections available to defendants at trial do not apply at revocation hearings. Thus, the exclusionary rule has been held inapplicable to revocation hearings. This is in contrast to a recent district court decision, Standlee v. Rhay, where it was held that because of the punitive nature of a revocation hearing, it should be treated in some respects as equivalent to a criminal proceeding. These contrasting results are not as inconsistent as they may seem at first glance, but may be harmonized, to some extent, through an analysis of the principles underlying the respective doctrines. Although revocation hearings often present both exclusionary rule and collateral estoppel problems, these are essentially distinct legal concepts