Measure homology and singular homology are isometrically isomorphic

Measure homology is a variation of singular homology designed by Thurston in his discussion of simplicial volume. Zastrow and Hansen showed independently that singular homology (with real coefficients) and measure homology coincide algebraically on the category of CW-complexes. It is the aim of this paper to prove that this isomorphism is isometric with respect to the l^1-seminorm on singular homology and the seminorm on measure homology induced by the total variation. This, in particular, implies that one can calculate the simplicial volume via measure homology -- as already claimed by Thurston. For example, measure homology can be used to prove the proportionality principle of simplicial volume.Comment: 20 pages, typos corrected, see also http://www.math.uni-muenster.de/u/clara.loeh/preprints.html, accepted by Mathematische Zeitschrift -- the original publication is available at www.springerlink.com (http://dx.doi.org/10.1007/s00209-005-0905-7

The Evolution of Judicial Power: How the Supreme Court Effectively Legalized Rape on Indian Reservations

According to the 2010 National Intimate Partner and Sexual Violence Survey, nearly one in five women in the United States have experienced sexual violence. While the statistics are staggering, the rate of sexual assault on Indian reservations is more than twice the national average. According to the Department of Justice, one in three American Indian and Alaska Native women have been raped or have experienced an attempted rape during their lifetime. Moreover, the primary assailants are males who are not members of tribal communities. Why has rape, perpetrated by non-Indian males, become effectively legalized on reservations? What explains tribal courts’ limited legal capacity to prosecute rape? I emphasize the pivotal Oliphant v. Suquamish Indian Tribe decision that changed the landscape of judicial power on reservations. The result has produced unintended consequences, which greatly diminished the legal capacity to prosecute sexual assault cases in tribal courts. Consequently, three phases of evolution in U.S. history indicate that rape was effectively legalized. These three phases of evolution are dependent on colonialism. The criminal behavior of non-Indian males can be explained through the historical evolution of judicial power, which has in effect legalized rape in tribal communities. An examination of the hidden institutional elements considers the evolutionary trajectory of interactions between the U.S. government and tribal reservations. This broader frame analysis provides new insights toward the impact of Oliphant on the lives of American Indian and Alaska Native women

Posturing by Romania’s political parties ahead of December elections shows that they are not just competing for power, but for their own survival

This month has seen massive rallies for Romania’s political parties ahead of parliamentary elections in December, with the European People’s Party holding its congress and the ruling USL alliance hosting an 80,000 strong rally. Clara Volintiru looks at this political posturing between the rival factions of the President and Prime Minister, and argues that these rallies ignore the general political disenchantment of most Romanians, and that there is a real risk of significant voter apathy come the December elections

Justice online: a new kind of justice?

It is a fact that mediation and other alternative dispute resolution means are becoming increasingly popular. Actually, governments are encouraging people to use them instead of going to Court, as they are quicker, cheaper and more informal than trials, and can be implemented using internet. The author focus on the analysis of the structure and purposes of mediation, in particular. The paper aims to discuss and understand what kind of justice, if any, is offered by alternative dispute resolution

ttˉt\bar{t} + ZZ / WW / ttˉt\bar{t} at ATLAS

The newest results from the ATLAS Collaboration for the production of a top-quark pair in association with a $Z$ or $W$ boson, and for the production of four top quarks, are summarised in these proceedings. The measurements were performed with 36.1 fb$^{-1}$ of proton-proton collision data from the Large Hadron Collider at a centre-of-mass energy of 13 TeV.Comment: 7 pages, 3 figures, TOP2018 Conference Proceeding

Finite functorial semi-norms and representability

Functorial semi-norms are semi-normed refinements of functors such as singular (co)homology. We investigate how different types of representability affect the (non-)triviality of finite functorial semi-norms on certain functors or classes. In particular, we consider representable functors, generalised cohomology theories, and so-called weakly flexible homology classes in singular homology and l1-homology.Comment: 18 pages; v3: small changes as suggested by the referee; v2: clarified Example 4.3, added referenc