scholarly journals Equivariant Differential Characters and Symplectic Reduction

2009 ◽  
Vol 289 (2) ◽  
pp. 777-801 ◽  
Author(s):  
Eugene Lerman ◽  
Anton Malkin
Keyword(s):  
Symplectic Reduction ◽  
Differential Characters

Symplectic Reduction of the Minimally Coupled Massless Superparticle in D=10

1990 ◽  
pp. 693-701
Author(s):  
John Harnad ◽  
Joel A. Shapiro ◽  
Steven Shnider ◽  
Cyrus C. Taylor
Keyword(s):  
Symplectic Reduction

scholarly journals Lefschetz-Pontrjagin duality for differential characters

2001 ◽  
Vol 73 (2) ◽  
pp. 145-159 ◽  
Author(s):  
REESE HARVEY ◽  
BLAINE LAWSON
Keyword(s):  
Duality Theorem ◽  
Manifolds With Boundary ◽  
Dense Range ◽  
Differential Characters ◽  
Alpha Beta ◽  
Duality Mappings ◽  
Central Result

A theory of differential characters is developed for manifolds with boundary. This is done from both the Cheeger-Simons and the deRham-Federer viewpoints. The central result of the paper is the formulation and proof of a Lefschetz-Pontrjagin Duality Theorem, which asserts that the pairing <img src="http:/img/fbpe/aabc/v73n2/fo1.gif" alt="fo1.gif (867 bytes)"> given by (alpha, beta) <img SRC="http:/img/fbpe/aabc/v73n2/m1img7.gif"> (alpha * beta) [X] induces isomorphisms <img src="http:/img/fbpe/aabc/v73n2/fo2.gif" alt="fo2.gif (1110 bytes)"> <img src="http:/img/fbpe/aabc/v73n2/fo3.gif" alt="fo3.gif (1086 bytes)"> onto the smooth Pontrjagin duals. In particular, <img SRC="http:/img/fbpe/aabc/v73n2/m1img13.gif"> and <img SRC="http:/img/fbpe/aabc/v73n2/m1img13a.gif"> are injective with dense range in the group of all continuous homomorphisms into the circle. A coboundary map is introduced which yields a long sequence for the character groups associated to the pair (X, <img SRC="http:/img/fbpe/aabc/v73n2/m1img14.gif">X). The relation of the sequence to the duality mappings is analyzed.

scholarly journals A new species of Gaurax from the Czech Republic (Diptera, Chloropidae)

ZooKeys ◽  
2018 ◽  
Vol 803 ◽  
pp. 131-140
Author(s):  
Štěpán Kubík ◽  
Miroslav Barták
Keyword(s):  
Czech Republic ◽  
New Species ◽  
The Czech Republic ◽  
European Species ◽  
Differential Characters ◽  
A New Species

Gauraxsiostrzonekisp. n.(Diptera, Chloropidae) is described from the Czech Republic and the main differential characters are illustrated. A key to the European species of the genus is provided.

Symplectic Reduction for Cotangent Groupoids

2021 ◽  
Vol 11 (03) ◽  
pp. 323-329
Author(s):  
远莉 戴
Keyword(s):  
Symplectic Reduction

Chalcidoidea of Iran (Insecta: Hymenoptera)

2021 ◽  
Keyword(s):  
Biological Control ◽  
Species Diversity ◽  
Phylogenetic Relationships ◽  
Parasitoid Species ◽  
Number Of Species ◽  
The Family ◽  
Differential Characters ◽  
Biological Attributes

Abstract Within Hymenoptera, the superfamily Chalcidoidea (chalcidoid wasps) is the second largest superfamily after Ichneumonoidea. Because of the preponderance of parasitoid species, Chalcidoidea is one of the most important groups in applied biological control. This book provides a comprehensive, accurate checklists for the chalcidoid fauna of Iran. The species listed in each family chapter include all the species recorded in the literature from Iran through 2019, with one exception as noted in Chapter 10 (Eurytomidae). Each family chapter includes differential characters to distinguish the family, hypothesized phylogenetic relationships with other families, and general biological attributes of the family. Previous cataloguing efforts of the Iranian fauna for the family are summarized, as well as the information included in the checklist of species for the family. This summary information includes the number of species recorded from Iran, any newly recorded species, a comparison of the Iranian fauna with those of adjacent countries, and major host attributes of the family in Iran. Also included for each species record are host records and plant associates in Iran, when known, and additional comments as necessary. The final chapter tabulates the species diversity of Iranian Chalcidoidea by family, the species newly exclude from Iran, the species presently considered as endemic to Iran and the number of species of each family that are known from each of the 31 provinces that comprise Iran. Because of the importance of chalcidoids for biological control of pests in Iran, host information for parasitoid species that is provided throughout the chapters is synthesized in an Appendix at the end of the book.

Family Torymidae Walker, 1833.

2021 ◽  
pp. 367-384
Author(s):  
Marina D. Zerova ◽  
Petr Janšta ◽  
Hassan Ghahari ◽  
Victor N. Fursov ◽  
Gary A. P. Gibson ◽  
...  
Keyword(s):  
Eastern Europe ◽  
Phylogenetic Relationships ◽  
Geographical Region ◽  
Western Asia ◽  
The Family ◽  
Differential Characters ◽  
Southern Caucasus ◽  
Biological Attributes ◽  
Caucasus Mountains ◽  
Political Units

Abstract This chapter includes differential characters to distinguish the family Torymidae (Chalcidoidea), hypothesized phylogenetic relationships with other families, and general biological attributes of the family. Previous cataloguing efforts of the Iranian fauna for the family are summarized, as well as the information included in the checklist of species for the family. This summary information includes the number of species recorded from Iran, any newly recorded species, a comparison of the Iranian fauna with those of adjacent countries, and major host attributes of the family in Iran. For each species record, reference is included to catalogues that previously reported presence of the species in Iran, including Noyes (2019), distribution in Iran by province and extra-limital distribution by country. In addition to currently recognized countries, previously recognized political units are also included such as Yugoslavia and USSR, as well as some non-political regions such as Caucasus and Transcaucasus (a geographical region in the vicinity of the southern Caucasus Mountains on the border of Eastern Europe and Western Asia that roughly corresponds to present-day Georgia, Armenia and Azerbaijan). Also included for each species record are host records and plant associates in Iran, when known, and additional comments as necessary.

scholarly journals Central Extensions of Lie Groups Preserving a Differential Form

2020 ◽  
Author(s):  
Tobias Diez ◽  
Bas Janssens ◽  
Karl-Hermann Neeb ◽  
Cornelia Vizman
Keyword(s):  
Lie Groups ◽  
Lie Algebra ◽  
Lie Group ◽  
Differential Form ◽  
Integral Form ◽  
Symplectic Manifolds ◽  
Central Extensions ◽  
Mapping Space ◽  
Canonical Class ◽  
Differential Characters

Abstract Let $M$ be a manifold with a closed, integral $(k+1)$-form $\omega $, and let $G$ be a Fréchet–Lie group acting on $(M,\omega )$. As a generalization of the Kostant–Souriau extension for symplectic manifolds, we consider a canonical class of central extensions of ${\mathfrak{g}}$ by ${\mathbb{R}}$, indexed by $H^{k-1}(M,{\mathbb{R}})^*$. We show that the image of $H_{k-1}(M,{\mathbb{Z}})$ in $H^{k-1}(M,{\mathbb{R}})^*$ corresponds to a lattice of Lie algebra extensions that integrate to smooth central extensions of $G$ by the circle group ${\mathbb{T}}$. The idea is to represent a class in $H_{k-1}(M,{\mathbb{Z}})$ by a weighted submanifold $(S,\beta )$, where $\beta $ is a closed, integral form on $S$. We use transgression of differential characters from $ S$ and $ M $ to the mapping space $ C^\infty (S, M) $ and apply the Kostant–Souriau construction on $ C^\infty (S, M) $.

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