Differential characters on curves

2011 ◽  
pp. 111-123
Author(s):  
Alexandru Buium
Keyword(s):  
Differential Characters

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.

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) $.

Family Tetracampidae Förster, 1856.

2021 ◽  
pp. 363-366
Author(s):  
Gary A. P. Gibson ◽  
Hassan Ghahari ◽  
Mikdat Doğanlar
Keyword(s):  
Phylogenetic Relationships ◽  
Number Of Species ◽  
The Family ◽  
Differential Characters ◽  
Biological Attributes ◽  
Political Units

Abstract This chapter includes differential characters to distinguish the family Tetracampidae (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. Also included for each species record are host records and plant associates in Iran, when known, and additional comments as necessary.

New lectotypifications and new synonyms in Festuca (Poaceae, Pooideae, Loliinae) from the Central Andes

Phytotaxa ◽  
2016 ◽  
Vol 247 (4) ◽  
pp. 247 ◽  
Author(s):  
JUAN C. OSPINA
Keyword(s):  
Morphological Characters ◽  
Central Andes ◽  
Andes Mountains ◽  
Valid Species ◽  
Second Step ◽  
New Synonyms ◽  
The Andes ◽  
New Synonym ◽  
Differential Characters ◽  
Anatomical Characters

New lectotypifications and new synonyms are provided as a result of a systematic study of the genus Festuca from the Central Andes. In the Andes mountains of Argentina, Bolivia, and Chile, several species of Festuca are dominant components of the grasslands and high Andean steppes. Festuca circinata and F. dissitiflora occur in this area and were described based on morphological characters. Some authors have considered F. circinata as a valid species while others have treated it as a synonym of F. dissitiflora, together with F. dissitiflora var. loricata , F. dissitiflora var. villipalea, and F. erecta var. aristulata. In this study, a review of the taxonomy and nomenclature of F. castilloniana, F. circinata, and F. potosiana was performed, and their morphological and anatomical characters were compared with F. dissitiflora. Based on morphoanatomical and epidermal characters, this study contributes to the delimitation of F. circinata and F. dissitiflora. Nomenclatural notes and new anatomical and epidermal descriptions are included for these species. Differential characters between F. circinata and F. dissitiflora are discussed and F. circinata is restored as a valid species for Argentina. Festuca castilloniana and F. potosiana are synonymised under F. dissitiflora. Festuca dissitiflora var. loricata, F. dissitiflora var. villipalea, and F. erecta var. aristulata are excluded from the synonymy of F. dissitiflora and it is suggested that these names should be subordinate under F. fiebrigii. Festuca stuckertii is proposed as a new synonym of F. uninodis. Lectotypes are designated for the names F. argentinensis, F. dissitiflora, F. nemoralis and F. parodii, and second-step lectotypes are designated for the names F. circinata and F. ampliflora.

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