TWISTED CONJUGACY CLASSES IN R. THOMPSON`S GROUP F

In this article, we prove that any automorphism of R. Thompson`s group F has infinitely many twisted conjugacy classes. The result follows from the work of Brin, together with standard facts about R. Thompson`s group F, and elementary properties of the Reidemeister numbers.

Twisted conjugacy classes in nilpotent groups

A group is said to have the R(infinity) property if every automorphism has an infinite number of twisted conjugacy classes. We study the question whether G has the R(infinity) property when G is a finitely generated torsion-free nilpotent group. As a consequence, we show that for every positive integer n >= 5, there is a compact nilmanifold of dimension n on which every homeomorphism is isotopic to a fixed point free homeomorphism. As a by-product, we give a purely group theoretic proof that the free group on two generators has the R(infinity) property. The R(infinity) property for virtually abelian and for C-nilpotent groups are also discussed.

REIDEMEISTER SPECTRUM FOR METABELIAN GROUPS OF THE FORM Q(n) x Z AND Z[1/p](n) x Z, p PRIME

In this paper, we study the Reidemeister spectrum for metabelian groups of the form Q(n) x Z and Z[1/p](n) x Z. Particular attention is given to the R(infinity)-property of a subfamily of these groups.

SIGMA THEORY AND TWISTED CONJUGACY CLASSES

Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely generated nonpolycyclic groups G that fall into one of the following classes: nilpotent-by-abelian groups of type FP(infinity); groups G/G `` of finite Prufer rank; groups G of type FP(2) without free nonabelian subgroups and with nonpolycyclic maximal metabelian quotient; some direct products of groups; or the pure symmetric automorphism group. Using a different argument we show that the result also holds for 1-ended nonabelian nonsurface limit groups. In some cases, such as with the generalized Thompson`s groups F(n,0) and their finite direct products, H = Aut(G).

Twisted conjugacy classes in symplectic groups, mapping class groups and braid groups (with an appendix written jointly with Francois Dahmani)

We prove that the symplectic group Sp(2n, Z) and the mapping class group Mod(S) of a compact surface S satisfy the R(infinity) property. We also show that B(n)(S), the full braid group on n-strings of a surface S, satisfies the R(infinity) property in the cases where S is either the compact disk D, or the sphere S(2). This means that for any automorphism phi of G, where G is one of the above groups, the number of twisted phi-conjugacy classes is infinite.

GROUND-STATE-ENERGY OF SINGULAR POTENTIALS

It is shown that for singular potentials of the form lambda/r(alpha),the asymptotic form of the wave function both at r --> infinity and r --> 0 plays an important role. Using a wave function having the correct asymptotic behavior for the potential lambda/r(4), it is, shown that it gives the exact ground-state energy for this potential when lambda --> 0, as given earlier by Harrell [Ann. Phys. (NY) 105, 379 (1977)]. For other values of the coupling parameter X, a trial basis;set of wave functions which also satisfy the correct boundary conditions at r --> infinity and r --> 0 are used to find the ground-state energy of the singular potential lambda/r(4) It is shown that the obtained eigenvalues are in excellent agreement with their exact ones for a very large range of lambda values.

Bi-Lipschitz A-equivalence of K-equivalent map-germs

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Argaric Sociology: Sex and Death

The detailed, rich and diverse Argaric funerary record offers an opportunity to explore social dimensions that usually remain elusive for prehistoric research, such us social rules on kinship rights and obligations, sexual tolerance and the role of funerary practices in preserving the economic and political organization. This paper addresses these topics through an analysis of the social meaning of Argaric double tombs by looking at body treatment and composition of grave goods assemblages according to gender and class affiliation. The Argaric seems to have been a conservative society, scarcely tolerant regarding homosexuality, and willing to celebrate ancestry associated to certain places as a means of asserting residence and property rights.

Generalized property R and the Schoenflies Conjecture

There is a relation between the generalized Property R Conjecture and the Schoenflies Conjecture that suggests a new line of attack on the latter. The new approach gives a quick proof of the genus 2 Schoenflies Conjecture and suffices to prove the genus 3 case, even in the absence of new progress on the generalized Property R Conjecture.

Parallel Research, Multiple Intellectual Property Right Protection Instruments, and the Correlation among R&D Projects, September 2005

The choice of a research path in attacking scientific and technological problems is a significant component of firms’ R&D strategy. One of the findings of the patent races literature is that, in a competitive market setting, firms’ noncooperative choices of research projects display an excessive degree of correlation, as compared to the socially optimal level. The paper revisits this question in a context in which firms have access to trade secrets, in addition to patents, to assert intellectual property rights (IPR) over their discoveries. We find that the availability of multiple IPR protection instruments can move the paths chosen by firms engaged in an R&D race toward the social optimum.

Intellectual Property Rights and Crop-Improving R&D under Adaptive Destruction, June 2007

This paper studies how the strength of intellectual property rights (IPRs) affects investments in biological innovations when the value of an innovation is stochastically reduced to zero because of the evolution of pest resistance. We frame the problem as a research and development (R&D) investment game in a duopoly model of sequential innovation. We characterize the incentives to invest in R&D under two competing IPR regimes, which differ in their treatment of the follow-on innovations that become necessary because of pest adaptation. Depending on the magnitude of the R&D cost, ex ante firms might prefer an intellectual property regime with or without a “research exemption” provision. The study of the welfare function that also accounts for benefit spillovers to consumers—which is possible analytically under some parametric conditions, and numerically otherwise—shows that the ranking of the two IPR regimes depends critically on the extent of the R&D cost.

Desert tortoise habitat conservation : hearing before the Subcommittee on Forests and Public Land Management of the Committee on Energy and Natural Resources, United States Senate, One Hundred Seventh Congress, first session, on H.R. 880, to provide for the acquisition of property in Washington County, Utah, for implementation of a desert tortoise habitat conservation plan, May 10, 2001.

Shipping list no.: 2001-0272-P.