Chapter 6 ties invertible topological phases to extensions of the original Lieb–Schultz–Mattis theorem. A review is made of the original Lieb–Schultz–Mattis theorem and how it has been refined under the assumption that a continuous symmetry holds. Two extensions of the Lieb–Schultz–Mattis theorem are given that apply to the Majorana chains from Chapter 5 when protected by discrete symmetries. To this end, it is necessary to introduce the notion of projective representations of symmetries and their classifications in terms of the second cohomology group. A precise definition is given of fermionic invertible topological phases and how they can be classified by the second cohomology group in one-dimensional space. Stacking rules of fermionic invertible topological phases in one-dimensional space are explained and shown to deliver the degeneracies of the boundary states that are protected by the symmetries.

Despite Kenya’s transformative and progressive 2010 Constitution, it is still grappling with a hybrid democracy, displaying both authoritarian and democratic traits. Scholars attribute this status to several factors, with a prominent one being the domination of the political order and wielding of political power by a few individuals and families with historical ties to patronage networks and informal power structures. The persisting issues of electoral fraud, widespread corruption, media harassment, weak rule of law and governance challenges further contribute to the hybrid democracy status. While the 2010 Constitution aims to restructure the state and enhance democratic institutions, the transition process is considered incomplete, especially since the judiciary’s role of judicial review is mostly faced with the difficult task of countering democratic regression. Moreover, critical institutions such as the Independent Electoral and Boundaries Commission (IEBC) have faced criticism due to corruption scandals and perceptions of partisanship, eroding public trust in their ability to oversee fair elections effectively.

Black Americans and Indians built many connections to combat White supremacy and they positioned the Black American and Indian struggle as part of a global movement for equality, as W. E. B. Du Bois and Lala Lajpat Rai commonly emphasized. They utilized each other to modify their aspirations for their respective societies and achieve a meaningful social impact, particularly in the US. However, this impact largely occurred after Indian independence through the efforts of Black radicals such as Du Bois, Paul Robeson, and William Patterson who identified India as a source of sympathy for the Black American cause because Indians were similarly victimized by White supremacy under the British Raj.

Caste was not a colonial invention and, therefore, the end of British colonialism did not result in its annihilation and some caste elements of British colonialism have remained in India. One of the most striking parallels regarding how African Americans and Dalits remain marginalized is the persistence of “criminal castes.” Although some low-caste Indians could access education, land, and better jobs during the British Raj, occupational specialization was generally accepted as a defining characteristic of castes and tribes, even to the extent of defining certain tribal communities as “habitually” criminal under the Criminal Tribes Act. Originally passed by the British government in 1871, the British used the act to categorize some communities across the country as “born criminals,” irrespective of their criminal precedents. The act required adult male members of such groups to have weekly meetings with the local police and they were not allowed to leave their villages without permission. The categorizations had no basis in criminal evidence and were merely based upon racial and caste stereotypes. The British government initially proposed the act to reform “born criminals” through labor. However, when these “born criminals” attempted to make a living like members from other castes, they struggled to find work outside the settlement because of public prejudice and marginalization.

The Introduction reviews the widely shared understanding of Schopenhauer as an apolitical thinker. It then articulates the challenge to this view. Schopenhauer, this book argues, defined politics as the rational management of perpetual human strife. The Introduction lays out the two main steps for recovering the full scope of Schopenhauer’s political thought. First, his attitude to politics must be historically contextualized. Against the backdrop of his era and the political ideas of other thinkers, the individual profile and polemical significance of Schopenhauer’s conception of politics come into view more clearly. Second, his textually dispersed political ideas must be assembled into a recognizable whole. Many of Schopenhauer’s reflections on political skills, values, ideologies, and regimes can be found in sections that do not explicitly deal with politics, and his core conception of politics becomes visible through a series of contrasts between politics and religion, politics and morality, and politics and sociability.

Mindfulness has evolved from a psychological intervention to a transformative lifestyle practice, offering profound benefits for mental health and cognition. By focusing on the present moment, mindfulness cultivates self-awareness and effective coping mechanisms, thereby reducing stress and promoting emotional regulation. Evidence suggests that structured mindfulness training enhances emotional wellbeing, mitigating anxiety and depression, and improving sleep quality, even during periods of heightened stress like the COVID-19 pandemic. In educational settings, mindfulness contributes to reduced depression and anxiety while enhancing academic performance. Moreover, it fosters resilience and job satisfaction among professionals in high-stress environments. Cognitive benefits of mindfulness include improvements in executive function, attentional control, and working memory, even in neurological and neuropsychiatric disorders. Neuroscientific studies reveal structural and functional brain changes in regions involved in attention and emotion regulation. Embracing mindfulness as a regular practice empowers individuals to navigate life’s challenges with resilience, promoting mental health, creativity, and overall quality of life.

This chapter explores one of the drastic effects of Sierra Leone’s Sexual Offences Act (SOA) by analysing the cases of young men and boys imprisoned for sleeping with their girlfriends. Within Pademba Road, Freetown’s central prison, young men face extreme punishment meant to sever pre-prison ties. SOA sentences result in isolation and separation from the outside world and other prisoners. LB and Larry, the cases analysed in this chapter, employ different tactics to survive, partially adapting as docile prisoners, partially engaging in resistance tactics. The chapter highlights the informal power structures within the prison, where ‘red bands’ hold sway, often surpassing the authority of guards. The text also points out the unpredictability and resource challenges within Sierra Leone’s criminal justice system, impacting marginalised individuals. The chapter portrays young men navigating the SOA’s consequences, challenging the legal system’s effectiveness, and raising questions about its impact on relationships and intimacy.

This chapter goes through a list of potential thermal regimes occurring prior to the development of the strike-slip setting or transform margin. These have a strong impact on the thermal regime among all controlling factors. This is due to the fact that the thermal regime affects the host continental lithosphere in many different aspects, such as its thickness, metamorphic reactions, melt formation, rheological zonation, and mechanical behavior. Following a brief summary of basic concepts of heat transport and generation, and heat flow presently observed at the Earth’s surface, the chapter discusses thermal regimes and temperature distribution with depth that can exist in continental lithosphere affected by transform margin formation. It sets the stage for the subsequent evolution, which is strongly dependent on the initial subsurface temperature field. Although this influence progressively diminishes as the transform margin evolves, the knowledge of pre-existing thermal regimes may also help to understand spatial variations along a specific transform margin segment and present-day differences between transform margins.

This chapter explores developments in hemispheric and transamerican studies by grounding discussions of colonialism and incommensurability in narrations of place-names. It moves from the Pacific to the Midwest, using Commodore David Porter’s Journal of a Cruise Made to the Pacific Ocean, from the War of 1812, as a case study. Porter is of note not only because he was an important source for Herman Melville’s Pacific writings but also because his military travel writings sought to make the Marquesas part of the US political and popular imaginary. In renaming-to-claim the islands, Porter worked to undermine Indigenous epistemologies and histories. The chapter then turns to the Midwest, examining the Latin American place-names across the region – names that offer a nineteenth-century prehistory to accounts of widespread Midwestern Latinx presence. Surprisingly, stories of Porter’s battle off the coast of Chile in Journal of a Cruise have fed an imperialist “Latin American mapping” of Indiana through the naming of the city of Valparaiso, in Porter County. Using stories of place naming from the Indigenous Pacific and Latinx Midwest, the chapter highlights the vital necessity of hemispheric and transamerican literary studies for the nineteenth century.

“Philosophers of the Cabal” inaugurates a line of inquiry devoted to the Volk (people). A powerful critic of Kantian anthropology, Johann Gottfried Herder argued that the “spirit of a people [Volksgeist]” is grounded in a common structure of sensibility or Sinnlichkeit. This shared sensibility derives in part from the notion of the sensus communis theorized by British empiricists in the early eighteenth century. After tracing the influence of British aesthetics on Herder, the chapter moves forward to consider E. B. Tylor, a towering figure of Victorian anthropology known for the evolutionary theories that displaced Herder’s diversitarian model. I show that Tylor actually retained key Herderian premises regarding collective sensation, which modernists like W. B. Yeats then incorporated into a primitivist style. Hence the communalist aesthetics running from Shaftesbury through Herder and Tylor leads ultimately to modernists who came of age during the fin-de-siècle.

The preceding treatment, perhaps particularly the final chapter, may leave the reader with lingering questions. In these closing words I offer some indication of how I sense these unresolved questions may land. The questions may be divided into two kinds. The first kind say, surely you have gone too far? The second say, what if you were to go further? Unsurprisingly most attention settles on the former; but my interest is mostly on the latter.

This starred (omittable) chapter is devoted to non-separable versions of results already proved in the more tractable separable context. As the star indicates, the results here are aimed more at the specialist topologist than at the general mathematical reader, our usual intended audience.