Topic
String group
About: String group is a research topic. Over the lifetime, 55 publications have been published within this topic receiving 500 citations.
Papers published on a yearly basis
Papers
TL;DR: In this paper, the authors provide a model of the string group as a central extension of finite-dimensional 2-groups in the bicategory of Lie groupoids, left-principal bibundles, and bibundle maps.
Abstract: We provide a model of the String group as a central extension of finite-dimensional 2‐groups in the bicategory of Lie groupoids, left-principal bibundles, and bibundle maps. This bicategory is a geometric incarnation of the bicategory of smooth stacks and generalizes the more naive 2‐category of Lie groupoids, smooth functors and smooth natural transformations. In particular this notion of smooth 2‐group subsumes the notion of Lie 2‐group introduced by Baez and Lauda [5]. More precisely we classify a large family of these central extensions in terms of the topological group cohomology introduced by Segal [56], and our String 2‐group is a special case of such extensions. There is a nerve construction which can be applied to these 2‐groups to obtain a simplicial manifold, allowing comparison with the model of Henriques [23]. The geometric realization is an A1 ‐space, and in the case of our model, has the correct homotopy type of String.n/. Unlike all previous models [58; 60; 33; 23; 7] our construction takes place entirely within the framework of finitedimensional manifolds and Lie groupoids. Moreover within this context our model is characterized by a strong uniqueness result. It is a canonical central extension of Spin.n/. 57T10, 22A22, 53C08; 18D10 The String group is a group (or A1 ‐space) which is a 3‐connected cover of Spin.n/. It has connections to string theory, the generalized cohomology theory topological modular forms (tmf ), and to the geometry and topology of loop space. Many of these relationships can be explored homotopy theoretically, but a geometric model of the String group would help provide a better understanding of these subjects and their interconnections. Over the past decade there have been several attempts to provide geometric models of the String group; see Stolz [58], Stolz and Teichner [60], Jurco [33], Henriques [23] and Baez, Stevenson, Crans and Schreiber [7]. The most recent of these use the language of higher categories, and consequently string differential geometry also provides a test case for the emerging field of higher categorical differential geometry; see Waldorf [64] and Sati, Schreiber and Stasheff [51; 52].
102 citations
Patent•
18 Sep 1997TL;DR: In this article, a memory cell array of a nonvolatile semiconductor memory device includes unit strings grouped into first strings belonging to a first string group and second string groups, each unit string has a memory cells for storing data in a non-volatile state Each first string is coupled between an associated bit line of a first bit line group and a first common source line.
Abstract: A memory cell array of a non-volatile semiconductor memory device includes unit strings grouped into first strings belonging to a first string group and second strings belonging to a second string group Each unit string has a memory cells for storing data in a non-volatile state Each first string is coupled between an associated bit line of a first bit line group and a first common source line whereas each second string is coupled between an associated bit line of a second bit line group and a second common source line The bit lines and the common source lines are made of different conductive layers In accordance with the invention, it is possible to achieve a less critical layout of sense amplifiers coupled to bit lines while easily performing a photolithography process as required in the manufacture of the memory device
89 citations
TL;DR: In this paper, the String 2-group is introduced as a special case of the topological group cohomology introduced by G. Segal, and a nerve construction which can be applied to these 2-groups to obtain a simplicial manifold.
Abstract: We provide a model of the String group as a central extension of finite-dimensional 2-groups in the bicategory of Lie groupoids, left-principal bibundles, and bibundle maps. This bicategory is a geometric incarnation of the bicategory of smooth stacks and generalizes the more na\"ive 2-category of Lie groupoids, smooth functors, and smooth natural transformations. In particular this notion of smooth 2-group subsumes the notion of Lie 2-group introduced by Baez-Lauda. More precisely we classify a large family of these central extensions in terms of the topological group cohomology introduced by G. Segal, and our String 2-group is a special case of such extensions. There is a nerve construction which can be applied to these 2-groups to obtain a simplicial manifold, allowing comparison with with the model of A. Henriques. The geometric realization is an $A_\infty$-space, and in the case of our model, has the correct homotopy type of String(n). Unlike all previous models our construction takes place entirely within the framework of finite dimensional manifolds and Lie groupoids. Moreover within this context our model is characterized by a strong uniqueness result. It is a unique central extension of Spin(n).
85 citations
TL;DR: In this paper, a model for the string group as an infinite-dimensional Lie group was constructed and extended by a contractible Lie group to a Lie 2-group model, and an explicit comparison of string structures for the two models was provided.
Abstract: We construct a model for the string group as an infinite-dimensional Lie group. In a second step we extend this model by a contractible Lie group to a Lie 2-group model. To this end we need to establish some facts on the homotopy theory of Lie 2-groups. Moreover, we provide an explicit comparison of string structures for the two models.
42 citations
TL;DR: In this article, a model for the string group as an infinite-dimensional Lie group was constructed, and the model was extended by a contractible Lie group to a Lie 2-group model.
Abstract: We construct a model for the string group as an infinite-dimensional Lie group. In a second step we extend this model by a contractible Lie group to a Lie 2-group model. To this end we need to establish some facts on the homotopy theory of Lie 2-groups. Moreover, we provide an explicit comparison of string structures for the two models and a uniqueness result for Lie 2-group models.
38 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2020 | 6 |
| 2019 | 5 |
| 2018 | 6 |
| 2017 | 6 |
| 2016 | 3 |