Добірка наукової літератури з теми "Basic bundle gerbe"

AbstractWe study bundle gerbes on manifolds M that carry an action of a connected Lie group G. We show that these data give rise to a smooth 2-group extension of G by the smooth 2-group of hermitean line bundles on M. This 2-group extension classifies equivariant structures on the bundle gerbe, and its non-triviality poses an obstruction to the existence of equivariant structures. We present a new global approach to the parallel transport of a bundle gerbe with connection, and use it to give an alternative construction of this smooth 2-group extension in terms of a homotopy-coherent version of the associated bundle construction. We apply our results to give new descriptions of nonassociative magnetic translations in quantum mechanics and the Faddeev–Mickelsson–Shatashvili anomaly in quantum field theory. We also propose a definition of smooth string 2-group models within our geometric framework. Starting from a basic gerbe on a compact simply-connected Lie group G, we prove that the smooth 2-group extensions of G arising from our construction provide new models for the string group of G.

The paper explains the internal phonological and lexical innovations in Taba language in North Maluku from historical linguistics perspective. 200 and 1000 basic and cultural vocabulary, respectively, have been collected using note-taking and recorded interviews in Taba language and other related languages, including Buli, Maba, Sawai, Gebe, and Gane. Data were analysed using horizontal approach, employing intralingual comparative-linking method. The analysis reveals that Taba language has nine phonological propensities which are unidentified in other languages in North Maluku. These include (1) realization of /s/ in the final position, preceded by dental consonants /d, t/; (2) omission, as opposed to appearance in other languages, of the first syllable; (3) realization of vowel /o/ in penultima sylable (otherwise i-o sequence in different syllables); 4) realization of consonant /h/ in ultima and penultima sylables; 5) realization of consonant /c/in the initial potition; 6) regular realization of vowel /a/ in the initial penultima syllable; 7) omission of the first syllable, followed by an addition of either a phoneme or syllable in the final position; 8) realization of /k/ in the final position; and 9) realization of /h/ in the central position. Meanwhile, the internal lexical innovation (the difference with the other five languages of South Halmahera is horizontal) can be observed in as such words that refer to awan ‘cloud’, baik ‘good’, belok ‘to turn’, gigit ‘to bite’, dekat ‘near’, ikat ‘bundle’, jahit ‘stitch’, jarum ‘needle’ and jika‘if’.Key words: internal innovations, historical linguistics, phonological innovations, lexical innovations.INOVASI INTERNAL BAHASA TABA DI MALUKU UTARA: PERSPEKTIF LINGUISTIK HISTORISAbstrakTulisan ini bertujuan menjelaskan inovasi internal aspek fonologi dan leksikal bahasa Taba di Maluku Utara dari perspektif studi linguistik historis. Data berupa 200 kosa kata dasar dan 1000 kosa kata budaya telah dikumpulkan dengan metode wawancara/cakap teknik catat dan rekam dalam bahasa Taba, dan lima bahasa lain yang sekerabatnya dengannya, yaitu Buli, Maba, Sawai, Gebe, dan Gane. Lalu, data dianalisis menggunakan pendekatan horizontal metode padan intralingual, teknik hubung-banding. Dalam bahasa Taba setidak-tidaknya memiliki sembilan kecenderungan fonologis yang tidak dimiliki oleh bahasa Halmahera Selatan lainnya. Yaitu, (1) merealisasikan bunyi /s/ pada posisi akhir yang diawali konsonan dental /d, t/; (2) mengalami penghilangan suku awal, sedangkan bahasa lain sebaliknya (muncul); (3) merealisasikan vokal /o/ (perendahan vokal) pada silabe penultima (atau pada urutan i-o pada silabe berbeda); (4) merealisasikan konsonan /h/ baik pada silabe penultima maupun ultima; (5) merealisasikan konsonan /c/ pada posisi awal; (6) merealisasikan vokal /a/ secara teratur pada silabe awal penultima; (7) terjadi penghilangan suku awal diikuti oleh penambahan fonem atau silabe pada posisi akhir; (8) merealisasikan /k/ pada posisi akhir; serta (9) merealisasikan bunyi /h/ pada posisi tengah. Adapun inovasi leksikal (perbedaannya dengan lima bahasa Halmahea Selatan lainnya secara horizontal) di antaranya dapat ditemukan pada kata yang bermakna ‘awan’, ‘baik’, ‘belok’, ‘gigit’, ‘dekat’, ‘ikat’, ‘jahit’, ‘jarum’, ‘jika, kalau’, dan sebagainya.Kata kunci: inovasi internal, linguistik historis, inovasi fonologi, dan inovasi leksikal.

Abstract Many bundle gerbes are either infinite-dimensional, or finite-dimensional but built using submersions that are far from being fibre bundles. Murray and Stevenson [‘A note on bundle gerbes and infinite-dimensionality’, J. Aust. Math. Soc.90(1) (2011), 81–92] proved that gerbes on simply-connected manifolds, built from finite-dimensional fibre bundles with connected fibres, always have a torsion $DD$ -class. I prove an analogous result for a wide class of gerbes built from principal bundles, relaxing the requirements on the fundamental group of the base and the connected components of the fibre, allowing both to be nontrivial. This has consequences for possible models for basic gerbes, the classification of crossed modules of finite-dimensional Lie groups, the coefficient Lie-2-algebras for higher gauge theory on principal 2-bundles and finite-dimensional twists of topological K-theory.

This thesis reviews bundle gerbe theory and the well-known basic bundle gerbe over SU(n). We introduce the cup product bundle gerbe, and show it is stably isomorphic to the pullback of the basic bundle gerbe by the Weyl map. This result enriches our understanding of the basic bundle gerbe, which has numerous applications in physics.
Thesis (MPhil) -- University of Adelaide, School of Mathematical Sciences, 2019

This book provides a systematic exposition of the theory of Fourier-Mukai transforms from an algebro-geometric point of view. Assuming a basic knowledge of algebraic geometry, the key aspect of this book is the derived category of coherent sheaves on a smooth projective variety. The derived category is a subtle invariant of the isomorphism type of a variety, and its group of autoequivalences often shows a rich structure. As it turns out — and this feature is pursued throughout the book — the behaviour of the derived category is determined by the geometric properties of the canonical bundle of the variety. Including notions from other areas, e.g., singular cohomology, Hodge theory, abelian varieties, K3 surfaces; full proofs and exercises are provided. The final chapter summarizes recent research directions, such as connections to orbifolds and the representation theory of finite groups via the McKay correspondence, stability conditions on triangulated categories, and the notion of the derived category of sheaves twisted by a gerbe.