An isovariant map is an equivariant map preserving the isotropy subgroups. In this paper, we develop an isovariant version of the Hopf classification theorem; namely, an isovariant homotopy classification result of G-...An isovariant map is an equivariant map preserving the isotropy subgroups. In this paper, we develop an isovariant version of the Hopf classification theorem; namely, an isovariant homotopy classification result of G-isovariant maps from free G-manifolds to representation spheres under a certain dimensional condition, the so-called Borsuk-Ulam inequality. In order to prove it, we use equivariant obstruction theory and the multidegree of an isovariant map.展开更多
The isovariant Borsuk Ulam constant cc of a compact Lie group G is defined to be the supremum of c ∈ R such that the inequalityc（dim V - dim V^C） ≤ dim W - dim W^Gholds whenever there exists a G-isovariant map f ...The isovariant Borsuk Ulam constant cc of a compact Lie group G is defined to be the supremum of c ∈ R such that the inequalityc（dim V - dim V^C） ≤ dim W - dim W^Gholds whenever there exists a G-isovariant map f ： S（V） → S（W） between G-representation spheres. In this paper, we shall discuss some properties of cG and provide lower estimates of cG of connected compact Lie groups, which leads us to some Borsuk-Ulam type results for isovariant maps. We also introduce and discuss the generalized isovariant Borsuk-Ulam constant c^-G for more general smooth G-actions on spheres. The result is considerably different from the case of linear actions.展开更多
Dynamics of the actin cytoskeleton are essential for pollen germination and pollen tube growth. ACTIN- DEPOLYMERIZlNG FACTORs （ADFs） typically contribute to actin turnover by severing/depolymerizing actin filaments....Dynamics of the actin cytoskeleton are essential for pollen germination and pollen tube growth. ACTIN- DEPOLYMERIZlNG FACTORs （ADFs） typically contribute to actin turnover by severing/depolymerizing actin filaments. Recently, we demonstrated that Arabidopsis subclass III ADFs （ADF5 and ADF9） evolved F-actin-bundling function from conserved F-actin-depolymerizing function. However, little is known about the physiological function, the evolutional significance, and the actin-bundling mechanism of these neo- functionalized ADFs. Here, we report that loss of ADF5 function caused delayed pollen germination, retarded pollen tube growth, and increased sensitive to latrunculin B （LatB） treatment by affecting the generation and maintenance of actin bundles. Examination of actin filament dynamics in living cells revealed that the bundling frequency was significantly decreased in adf5 pollen tubes, consistent with its biochem- ical functions. Further biochemical and genetic complementation analyses demonstrated that both the N- and C-terminal actin-binding domains of ADF5 are required for its physiological and biochemical functions. Interestingly, while both are atypical actin-bundling ADFs, ADF5, but not ADF9, plays an important role in mature pollen physiological activities. Taken together, our results suggest that ADF5 has evolved the function of bundling actin filaments and plays an important role in the formation, organization, and maintenance of actin bundles during pollen germination and pollen tube growth.展开更多
文摘An isovariant map is an equivariant map preserving the isotropy subgroups. In this paper, we develop an isovariant version of the Hopf classification theorem; namely, an isovariant homotopy classification result of G-isovariant maps from free G-manifolds to representation spheres under a certain dimensional condition, the so-called Borsuk-Ulam inequality. In order to prove it, we use equivariant obstruction theory and the multidegree of an isovariant map.
文摘The isovariant Borsuk Ulam constant cc of a compact Lie group G is defined to be the supremum of c ∈ R such that the inequalityc（dim V - dim V^C） ≤ dim W - dim W^Gholds whenever there exists a G-isovariant map f ： S（V） → S（W） between G-representation spheres. In this paper, we shall discuss some properties of cG and provide lower estimates of cG of connected compact Lie groups, which leads us to some Borsuk-Ulam type results for isovariant maps. We also introduce and discuss the generalized isovariant Borsuk-Ulam constant c^-G for more general smooth G-actions on spheres. The result is considerably different from the case of linear actions.
基金This work was supported by the National Basic Research Program （2014CB954203）, the National Natural Science Foundation of China （31670180, 31470283）, and the Fundamental Research Funds for the Cen- tral Universities （Izujbky-2016-bt05） to Y.X.
文摘Dynamics of the actin cytoskeleton are essential for pollen germination and pollen tube growth. ACTIN- DEPOLYMERIZlNG FACTORs （ADFs） typically contribute to actin turnover by severing/depolymerizing actin filaments. Recently, we demonstrated that Arabidopsis subclass III ADFs （ADF5 and ADF9） evolved F-actin-bundling function from conserved F-actin-depolymerizing function. However, little is known about the physiological function, the evolutional significance, and the actin-bundling mechanism of these neo- functionalized ADFs. Here, we report that loss of ADF5 function caused delayed pollen germination, retarded pollen tube growth, and increased sensitive to latrunculin B （LatB） treatment by affecting the generation and maintenance of actin bundles. Examination of actin filament dynamics in living cells revealed that the bundling frequency was significantly decreased in adf5 pollen tubes, consistent with its biochem- ical functions. Further biochemical and genetic complementation analyses demonstrated that both the N- and C-terminal actin-binding domains of ADF5 are required for its physiological and biochemical functions. Interestingly, while both are atypical actin-bundling ADFs, ADF5, but not ADF9, plays an important role in mature pollen physiological activities. Taken together, our results suggest that ADF5 has evolved the function of bundling actin filaments and plays an important role in the formation, organization, and maintenance of actin bundles during pollen germination and pollen tube growth.
