K-Theory and Formality Carlson, Jeffrey D
International mathematics research notices,
07/2023, Volume:
2023, Issue:
14
Journal Article
Peer reviewed
Open access
Abstract
We compare several notions of equivariant formality for complex K-theory with respect to a compact Lie group action, including surjectivity of the forgetful map and the weak equivariant ...formality of Harada–Landweber, and find all are equivalent under standard hypotheses. As a consequence, we present an expression for the equivariant K-theory of the isotropy action of $H$ on a homogeneous space $G/H$ in all the classical cases. The proofs involve mainly homological algebra and arguments with the Atiyah–Hirzebruch–Leray–Serre spectral sequence, but a more general result depends on a map of spectral sequences from Hodgkin’s Künneth spectral sequence in equivariant K-theory to that in Borel cohomology that seems not to have been otherwise defined. The hypotheses for the main structure result are analogous to a previously announced characterization of cohomological equivariant formality, first proved here, expanding on the results of Shiga and Takahashi.
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IZUM, KILJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
We employ a novel adaptation of self-construal theory to explain the theoretical basis of factors that influence organic food purchase decisions. Study 1 reveals that egoistic (e.g., personal health) ...and altruistic (e.g., environmental) considerations simultaneously predict consumers' organic attitudes and purchase intentions. Study 2 indicates that societal considerations play a more influential role for green/organic products. Study 3 tests advertising treatments utilizing egoistic and/or altruistic claims. Results show that an ad featuring both egoistic and altruistic appeals produces more favorable responses than either an egoistic treatment or a control ad, but is equally effective as an ad featuring altruistic claims.
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BFBNIB, IZUM, KILJ, NMLJ, NUK, PILJ, PNG, SAZU, UL, UM, UPUK
We prove a general structure theorem for the rational Borel equivariant cohomology ring of an equivariantly formal isotropy action, rederiving He’s recent computation of the equivariant cohomology of ...real Grassmannians as an illustration.
We completely characterize the pairs of connected Lie groups
G
>
K
such that
rk
G
-
rk
K
=
1
and the isotropy action of
K
on
G
/
K
is equivariantly formal. The analysis requires us to correct and ...extend an existing partial classification of homogeneous quotients
G
/
K
with the rational homotopy type of a product of an odd- and an even-dimensional sphere.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
This research investigates online consumer behavior in an e-commerce context with a focus on consumer online shopping cart use and subsequent cart abandonment. A model rooted in the Uses and ...Gratifications Theory, the Unified Theory of Acceptance and Use of Technology, and the concept of the purchase funnel is developed to explain the predicted relationships. Empirical findings based on clickstream data show that returning to an existing cart increases the subsequent cart use and decreases cart abandonment. Conversely, viewing clearance pages and viewing a large number of product reviews increases both cart use and cart abandonment. Browsing product pages decreases cart use, and increases cart abandonment. The moderating role of smartphone-based shopping is also examined, with the moderating effects primarily occurring early in the purchase funnel affecting cart use, and influencing cart abandonment to a smaller degree. Theoretical contributions and managerial implications for digital marketers are provided.
Atypical food intake is a primary cause of obesity and other eating and metabolic disorders. Insight into the neural control of feeding has previously focused mainly on signalling mechanisms ...associated with the hypothalamus, the major centre in the brain that regulates body weight homeostasis. However, roles of non-canonical central nervous system signalling mechanisms in regulating feeding behaviour have been largely uncharacterized. Acetylcholine has long been proposed to influence feeding owing in part to the functional similarity between acetylcholine and nicotine, a known appetite suppressant. Nicotine is an exogenous agonist for acetylcholine receptors, suggesting that endogenous cholinergic signalling may play a part in normal physiological regulation of feeding. However, it remains unclear how cholinergic neurons in the brain regulate food intake. Here we report that cholinergic neurons of the mouse basal forebrain potently influence food intake and body weight. Impairment of cholinergic signalling increases food intake and results in severe obesity, whereas enhanced cholinergic signalling decreases food consumption. We found that cholinergic circuits modulate appetite suppression on downstream targets in the hypothalamus. Together our data reveal the cholinergic basal forebrain as a major modulatory centre underlying feeding behaviour.
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IJS, KISLJ, NUK, SBMB, UL, UM, UPUK
This research sheds light on the theoretical mechanism behind consumer discounting of discounts and extends it to the online daily deals context. Based on advertising and behavioral pricing research, ...we develop and empirically test a conceptual model of the effects of discount level on consumer perceptions of discount credibility, the extent of discounting of discounts, and change in purchase intentions for online daily deal promotions as compared with price promotions offered directly by online stores. The findings offer important managerial recommendations for retailers and daily deal managers with respect to utilizing direct online price promotions and daily deal promotions.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
Long-range enhancer interactions critically regulate gene expression, yet little is known about how their coordinated activities contribute to CNS development or how this may, in turn, relate to ...disease states. By examining the regulation of the transcription factor NFIA in the developing spinal cord, we identified long-range enhancers that recapitulate NFIA expression across glial and neuronal lineages in vivo. Complementary genetic studies found that Sox9-Brn2 and Isl1-Lhx3 regulate enhancer activity and NFIA expression in glial and neuronal populations. Chromatin conformation analysis revealed that these enhancers and transcription factors form distinct architectures within these lineages in the spinal cord. In glioma models, the glia-specific architecture is present in tumors, and these enhancers are required for NFIA expression and contribute to glioma formation. By delineating three-dimensional mechanisms of gene expression regulation, our studies identify lineage-specific chromatin architectures and associated enhancers that regulate cell fate and tumorigenesis in the CNS.
Abstract Purpose This study was designed to contribute to the existing research on the coping behaviors, social support, and mental health outcomes in parents of children with epilepsy in the United ...States. Methods Participants included 152, predominantly Caucasian (89.5%), married (78.9%) women (95.4%). Via a web-based interface, mothers completed questionnaires assessing the impact of their child's disability on their family (i.e., severity of their child's disability, family burden, and personal stress), social resources (i.e., perceived social support), coping (i.e., emotion-focused and social support seeking), and adjustment (i.e., depression and anxiety). Results After controlling for demographic variables, mediational analysis revealed that mothers' perceptions of the severity of their child's disability were associated with decreased perceived social support, which was then related to higher reported levels of depression and anxiety. Similarly, low levels of perceived social support partially mediated the relation between family burden and depression, anxiety, and stress. Finally, mothers' perceptions of the severity of their children's disability and family burden were unrelated to their reports of emotion-focused or social support seeking coping. However, their use of emotion-focused and social support seeking behaviors was related to lower levels of depression. Conclusion Low levels of perceived social support may help to explain the mechanisms underlying the relation between mothers' perceptions of the severity of their child's disability and family burden on their mental health adjustment, such as depression and anxiety.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
Although firms leverage social media platforms such as Facebook to engage with customers, they often treat social media elements and other online marketing activities such as search engine ...advertising as stand-alone, rather than part of an integrated online activities system. Hence, it is important to systematically understand how specific elements of social media, signifying and representing behavioural manifestations of brand engagement, relate to other online activities. We study how three types of brand engagement on social media - affiliation, conversation and responsiveness - influence search engine advertising effectiveness, including click-through rate and conversion rate. Specifically, we find that affiliation, conversation and responsiveness increase click-through rate and conversion rate. Moreover, brand engagement on social media strengthens the relationships between advertisement rank and search engine advertising effectiveness.
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BFBNIB, IZUM, KILJ, NUK, PILJ, SAZU, UL, UM, UPUK
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