A Counterexample for Lightning Flash Modules over E(e1,e2)

We give a counterexample to Theorem 5 in Section 18.2 of Margolis' book, "Spectra and the Steenrod Algebra", and make remarks about the proofs of some later theorems in the book that depend on it. The counterexample is a module which does not split as a sum of lightning flash modules and free modules.Comment: 2 pages. Revision corrects a typo in the definition of M(n

Differentials in the homological homotopy fixed point spectral sequence

We analyze in homological terms the homotopy fixed point spectrum of a T-equivariant commutative S-algebra R. There is a homological homotopy fixed point spectral sequence with E^2_{s,t} = H^{-s}_{gp}(T; H_t(R; F_p)), converging conditionally to the continuous homology H^c_{s+t}(R^{hT}; F_p) of the homotopy fixed point spectrum. We show that there are Dyer-Lashof operations beta^epsilon Q^i acting on this algebra spectral sequence, and that its differentials are completely determined by those originating on the vertical axis. More surprisingly, we show that for each class x in the $^{2r}-term of the spectral sequence there are 2r other classes in the E^{2r}-term (obtained mostly by Dyer-Lashof operations on x) that are infinite cycles, i.e., survive to the E^infty-term. We apply this to completely determine the differentials in the homological homotopy fixed point spectral sequences for the topological Hochschild homology spectra R = THH(B) of many S-algebras, including B = MU, BP, ku, ko and tmf. Similar results apply for all finite subgroups C of T, and for the Tate- and homotopy orbit spectral sequences. This work is part of a homological approach to calculating topological cyclic homology and algebraic K-theory of commutative S-algebras.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-27.abs.htm

The Ancient Past: Learning a Language to Connect Materials with Users

Archives of the ancient world evince the longevity of our shared interests in preserving and documenting the culture, government, and knowledge of civilization. Whether studied by global travelers, classical archaeologists and historians, or filmmakers and television producers, archival materials from the ancient Mediterranean are contributing to collective memory, educational programming, and institutional collections. In this vein, the Program in Aegean Scripts and Prehistory (PASP) in the Department of Classics at The University of Texas at Austin fosters research and scholarship on the use of writing in Minoan Crete, Mycenaean Greece, and the island of Cyprus during the Bronze Age. There is a special focus on two early writing systems: Linear A and Cretan hieroglyphics (1900–1450 BCE) and Linear B (1400–1200 BCE). The program boasts an international base of researchers and users, and in recent years, staff have improved collection accessibility by reconfiguring physical spaces, advancing digitization projects, preserving endangered email accounts, and expanding the scope of collections to provide better access to these important materials.Classic

Good Fences Make Good Neighbors: Endogenous Property Rights in a Game of Conflict

This paper derives the conditions under which property rights can arise in an anarchy equilibrium. The creation of property rights requires that players devote part of their endowment to the public good of property rights protection. In the Nash equilibrium, players contribute zero to the protection of property rights. In contrast, a king who provides property rights protection paid for by a tax on endowments can completely eliminate conflict, but such a king has an incentive to take the surplus for himself. Thus players have an incentive to find a solution that keeps power in their own hands. In a social contract, players first credibly commit part of their endowments to providing property rights and then allocate the balance of their endowments between production and conflict. While property rights can arise under a social contract if the productivity of resources relative to the size of the population is sufficiently high, these property rights may be less than perfectly secure. Nevertheless, for sufficiently high productivity of resources relative to the size of the population, the social contract welfare dominates autocracy. Key Words:

Flexibility and development of mirroring mechanisms

The empirical support for the SCM is mixed. We review recent results from our own lab and others supporting a central claim of SCM that mirroring occurs at multiple levels of representation. By contrast, the model is silent as to why human infants are capable of showing imitative behaviours mediated by a mirror system. This limitation is a problem with formal models that address neither the neural correlates nor the behavioural evidence directly

On cyclic fixed points of spectra

For a finite p-group G and a bounded below G-spectrum X of finite type mod p, the G-equivariant Segal conjecture for X asserts that the canonical map X^G --> X^{hG} is a p-adic equivalence. Let C_{p^n} be the cyclic group of order p^n. We show that if the C_p Segal conjecture holds for a C_{p^n} spectrum X, as well as for each of its C_{p^e} geometric fixed points for 0 < e < n, then then C_{p^n} Segal conjecture holds for X. Similar results hold for weaker forms of the Segal conjecture, asking only that the canonical map induces an equivalence in sufficiently high degrees, on homotopy groups with suitable finite coefficients

Toda brackets and cup-one squares for ring spectra

In this paper we prove the laws of Toda brackets on the homotopy groups of a connective ring spectrum and the laws of the cup-one square in the homotopy groups of a commutative connective ring spectrum.Comment: 22 page

Some Remarks on the Root Invariant

We show how the root invariant of a product depends upon the product of the root invariants, give some examples of the equivariant definition of the root invariant, and verify a weakened form of the algebraic Bredon-Löffler conjecture