PurposeThe paper aims to determine the rational homotopy type of the total space of projectivized bundles over complex projective spaces using Sullivan minimal models, providing insights into the algebraic structure of these spaces. Design/methodology/approachThe paper utilises techniques from Sullivan’s theory of minimal models to analyse the differential graded algebraic structure of projectivized bundles. It employs algebraic methods to compute the Sullivan minimal model of and establish relationships with the base space. FindingsThe paper determines the rational homotopy type of projectivized bundles over complex projective spaces. Of great interest is how the Chern classes of the fibre space and base space, play a critical role in determining the Sullivan model ofP(E). We also provide the homogeneous space ofP(E)whenn = 2. Finally, we prove the formality ofP(E)over a homogeneous space of equal rank. Research limitations/implicationsLimitations may include the complexity of computing minimal models for higher-dimensional bundles. Practical implicationsUnderstanding the rational homotopy type of projectivized bundles facilitates computations in algebraic topology and differential geometry, potentially aiding in applications such as topological data analysis and geometric modelling. Social implicationsWhile the direct social impact may be indirect, advancements in algebraic topology contribute to broader mathematical knowledge, which can underpin developments in science, engineering, and technology with societal benefits. Originality/valueThe paper’s originality lies in its application of Sullivan minimal models to determine the rational homotopy type of projectivized bundles over complex projective spaces, offering valuable insights into the algebraic structure of these spaces and their associated complex vector bundles.
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Surfacing the complex conceptions of equity across making and tinkering spaces
PurposeRelatively few studies have examined the perspectives of informal learning facilitators who play key roles in cultivating an equitable learning environment for nondominant youth and families in making and tinkering spaces. This study aims to foreground the perspectives of facilitators and highlight the complexities and tensions that influence their equity work. Design/methodology/approachInterviews were conducted with facilitators of making and tinkering spaces across three informal learning organizations: a museum, a public library system and a network of community technology centers. This study then used a framework that examined equity along dimensions of access to what, for whom, based on whose values and toward what ends to analyze both the explicit and implicit conceptions of equity that surfaced in these interviews. FindingsAcross organizations, this study identified similarities and differences in facilitators’ conceptualizations of equity that were influenced by their different contexts and had implications for practice at each organization. Highlighting the complexity of enacting equity in practice, this study found moments when dimensions of equity came together in resonant ways, while other moments showed how dimensions can be in tension with each other. Practical implicationsThe complexity that facilitators must navigate to enact equity in their practice emphasizes the need for professional development and support for facilitators to deepen their conceptions and practices around equity beyond access – not just skill building in making and tinkering. Originality/valueThis study recognizes the important role that facilitators play in enabling equity-oriented participation in making and tinkering spaces and contributes the “on the ground” perspectives of facilitators to highlight the complexity and tensions of enacting equity in practice.
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- Award ID(s):
- 2005764
- PAR ID:
- 10542609
- Publisher / Repository:
- Emerald Publishing Limited
- Date Published:
- Journal Name:
- Information and Learning Sciences
- Volume:
- 124
- Issue:
- 7/8
- ISSN:
- 2398-5348
- Page Range / eLocation ID:
- 221 to 239
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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