Central extensions of mapping class groups from characteristic classes

Tangential structures on smooth manifolds, and the extension of mapping class groups they induce, admit a natural formulation in terms of higher (stacky) differential geometry. This is the literal translation of a classical construction in differential topology to a sophisticated language, but it has the advantage of emphasizing how the whole construction naturally emerges from the basic idea of working in slice categories. We characterize, for every higher smooth stack equipped with tangential structure, the induced higher group extension of the geometric realization of its higher automor- phism stack. We show that when restricted to smooth manifolds equipped with higher degree topological structures, this produces higher extensions of homotopy types of diffeomorphism groups. Passing to the groups of connected components, we obtain abelian extensions of mapping class groups and we derive sufficient conditions for these being central. We show as a special case that this provides an elegant re-construction of Segal’s approach to $\mathbb{Z}$ -extensions of mapping class groups of surfaces that provides the anomaly cancellation of the modular functor in Chern-Simons theory. Our construction generalizes Segal’s approach to higher central extensions of mapping class groups of higher dimensional manifolds with higher tangential structures, expected to provide the analogous anomaly cancellation for higher dimensional TQFTs

Applications of High-Resolution Gigapan Imagery in Mapping Fracture Systems: An Example from the Adirondack Basement Massif, New York

The Precambrian basement and overlying rocks that comprise the Adirondack massif have experienced significant brittle deformation with uplift over time. This has produced an extensive system of faults and fractures, which trends generally North-Northeast (N-NE) throughout the massif. The fault and fracture system is well-exposed at numerous outcrops, which has proven advantageous to characterizing it. In this study, fault density analysis was conducted on 12 well-exposed outcrops within the Piseco Lake shear zone in the southern Adirondacks. A combination of orientation measurements and high-resolution GigaPan panoramic imagery were collected at each outcrop, and together these data were used to generate fault density contour maps of the outcrops. The fault density and orientation data has been integrated into a new Google Earth-based interactive structural field map of the Adirondacks, which can be further built upon by the authors (and others) as additional field campaigns are completed. This study has successfully served as a proof-of-concept for the imaging and contouring method, and has demonstrated its efficacy to geological research. Characterizing the quantity and spatial distribution of bedrock joints and fractures has important implications in geological fields such as hydrogeology, resource exploration, geo-hazard assessment, and geo-engineering

The Face Semigroup Algebra of a Hyperplane Arrangement

This article presents a study of an algebra spanned by the faces of a hyperplane arrangement. The quiver with relations of the algebra is computed and the algebra is shown to be a Koszul algebra. It is shown that the algebra depends only on the intersection lattice of the hyperplane arrangement. A complete system of primitive orthogonal idempotents for the algebra is constructed and other algebraic structure is determined including: a description of the projective indecomposable modules; the Cartan invariants; projective resolutions of the simple modules; the Hochschild homology and cohomology; and the Koszul dual algebra. A new cohomology construction on posets is introduced and it is shown that the face semigroup algebra is isomorphic to the cohomology algebra when this construction is applied to the intersection lattice of the hyperplane arrangement.Comment: 37 pages, LaTeX; Added section 8.3B; Changed the wording of a few paragraphs in the introduction and abstract. No major change

Comparison between different approaches to modeling shallow landslide susceptibility: a case history in Oltrepo Pavese, Northern Italy

Abstract. On the 27 and 28 April 2009, the area of Oltrepo Pavese in northern Italy was affected by a very intense rainfall event that caused a great number of shallow landslides. These instabilities occurred on slopes covered by vineyards or recently formed woodlands and caused damage to many roads and one human loss. Based on aerial photographs taken immediately after the event and field surveys, more than 1600 landslides were detected. After acquiring topographical data, geotechnical properties of the soils and land use, susceptibility analysis on a territorial scale was carried out. In particular, different physically based models were applied to two contiguous sites with the same geological context but different typologies and sizes of shallow landslides. This paper presents the comparison between the ex-post results obtained from the different approaches. On the basis of the observed landslide localizations, the accuracy of the different models was evaluated, and the significant results are highlighted

Indexing Dan Searching Document Menggunakan Metode Semantic Suffix Tree Clustering Berbasis Android

Anroid smartphone device has been involved in user's way of living in this modern era. Smartphone device is used in user's daily activity such as reading and storing electronic document in Pdf, Word and other file formats. User might and frequently forgot elctronic document's directory in the smartphone.This research aims to help user to find documents that reflect user's keyword semantically or literally. Documents that reflect user keyword semantically or literaly will be shown. Various method is tested to minimize time use in clustering using suffix tree to semantic searching processes.This research finds that user could find documents in the smartphone that reflect user's keyword. Average time use for clustering about 100 documents containing 1000 word for each document is 686.7 seconds. User is able to search for document right after clustering process is done. Average time use for document searching is less than 2 seconds. Hence, thread implementation for processes decrease time consume greatly and the search result displayed to the user represents document content semantically

Batako Berlubang Geopolimer Berbahan Dasar Lumpur Sidoarjo

Lumpur Sidoarjo merupakan material yang sedang dikembangkan sebagai pengganti semen. Alasan digunakannya lumpur Sidoarjo adalah jumlahnya yang melimpah dan telah terbukti memiliki kandungan yang dapat menggantikan fungsi semen. Oleh karena itu sebaiknya lumpur Sidoarjo dijadikan sebagai produk jadi yang berguna, untuk masyarakat secara luas. Salah satu produk yang cocok diproduksi dari lumpur Sidoarjo adalah batako geopolimer. Batako geopolimer sendiri mempunyai beberapa kelebihan daripada batako pada umumnya, antara lain dapat mengurangi pelepasan gas CO2 ke atmosfer karena tidak menggunakan semen, sehingga lebih ramah terhadap lingkungan, selain itu bahan geopolimer memiliki ketahanan serangan dari luar. Untuk mengolah lumpur agar siap pakai dalam pembuatan batako, lumpur harus melewati beberapa tahapan, antara lain lumpur harus dijemur selama 24 jam, kemudian dimasukkan ke oven selama 24 jam. Setelah itu lumpur dibakar dengan suhu 650ºC selama 9 jam agar sifat lumpur menjadi amorf sehingga dapat digunakan. Lumpur kemudian digiling sampai melewati ayakan nomor 200. Setelah siap dipakai, lumpur dicampurkan dengan pasir, NaOH, serta sodium silikat dengan perbandingan tertentu untuk dijadikan campuran mortar untuk pembuatan batako. Dari hasil penelitian yang telah dilakukan, kuat tekan dan penyerapan air dari mortar menunjukkan hasil yang baik, Sehingga produk batako geopolimer memenuhi syarat batako pada umumnya