Let R be a right coherent ring and D^b（R-Mod） the bounded derived category of left R-modules. Denote by D^b（R-Mod）[GF,C] the subcategory of D^b（R-Mod） consisting of all complexes with both finite Gorenstein flat...Let R be a right coherent ring and D^b（R-Mod） the bounded derived category of left R-modules. Denote by D^b（R-Mod）[GF,C] the subcategory of D^b（R-Mod） consisting of all complexes with both finite Gorenstein flat dimension and cotorsion dimension and K^b（F∩C） the bounded homotopy category of flat cotorsion left R-modules. We prove that the quotient triangulated category D^b（R-Mod）[GF,C]/K^b（F∩C,） is triangle-equivalent to the stable category GF∩C of the Frobenius category of all Gorenstein fiat and cotorsion left R-modules.展开更多
An isoparametric family in the unit sphere consists of parallel isoparametric hypersurfaces and their two focal submanifolds.The present paper has two parts.The first part investigates topology of the isoparametric fa...An isoparametric family in the unit sphere consists of parallel isoparametric hypersurfaces and their two focal submanifolds.The present paper has two parts.The first part investigates topology of the isoparametric families,namely the homotopy,homeomorphism,or diffeomorphism types,parallelizability,as well as the Lusternik-Schnirelmann category.This part extends substantially the results of Wang(J Differ Geom 27:55-66,1988).The second part is concerned with their curvatures;more precisely,we determine when they have non-negative sectional curvatures or positive Ricci curvatures with the induced metric.展开更多
In this paper, we study the homotopy category of unbounded complexes of strongly copure projective modules with bounded relative homologies K;（SCP）.We show that the existence of a right recollement of K;（SCP） with...In this paper, we study the homotopy category of unbounded complexes of strongly copure projective modules with bounded relative homologies K;（SCP）.We show that the existence of a right recollement of K;（SCP） with respect to K;（SCP）, K;（SCP） and K;（SCP） has the homotopy category of strongly copure projective acyclic complexes as a triangulated subcategory in some case.展开更多
By assigning to each complex over a semi-simple ring two acyclicizations, we construct an explicit recollement for homotopy categories of a certain triangular matrix ring such that all the six triangle functors of the...By assigning to each complex over a semi-simple ring two acyclicizations, we construct an explicit recollement for homotopy categories of a certain triangular matrix ring such that all the six triangle functors of the recollement preserve acyclic complexes.展开更多
For an upper triangular matrix ring, an explicit ladder of height 2 of triangle functors between homotopy categories is constructed. Under certain conditions, the author obtains a localization sequence of homotopy cat...For an upper triangular matrix ring, an explicit ladder of height 2 of triangle functors between homotopy categories is constructed. Under certain conditions, the author obtains a localization sequence of homotopy categories of acyclic complexes of injective modules.展开更多
K. A. Hardie and K. H. Kamps investigated the track homotopy category H_B over a fixed space B ([1]). They have introduced two pairs of adjoint functors: P_B -|N_B and m_* -| m~*, where P_B:H_B→H^B, and m_*:H_A→H_B ...K. A. Hardie and K. H. Kamps investigated the track homotopy category H_B over a fixed space B ([1]). They have introduced two pairs of adjoint functors: P_B -|N_B and m_* -| m~*, where P_B:H_B→H^B, and m_*:H_A→H_B for a fixed map m: A→B. We have introduced a split fibration of categories L: H_b→H_B and proved L-|J, J-|L in [2]. This paper first extends P_B-|N_B to P_b_*-|N_Bb~# for any fixed map b:B→.Moreover we also extend these results to obtain two pairs of adjoint functors involving track homotopy categories H_b and H^b where H^b is the dual of H_b. One of our results is N_b-|P_b. This differs from P_B-|N_B.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11601433 and 11261050)the Postdoctoral Science Foundation of China(Grant No.2106M602945XB)Northwest Normal University(Grant No.NWNU-LKQN-15-12)
文摘Let R be a right coherent ring and D^b（R-Mod） the bounded derived category of left R-modules. Denote by D^b（R-Mod）[GF,C] the subcategory of D^b（R-Mod） consisting of all complexes with both finite Gorenstein flat dimension and cotorsion dimension and K^b（F∩C） the bounded homotopy category of flat cotorsion left R-modules. We prove that the quotient triangulated category D^b（R-Mod）[GF,C]/K^b（F∩C,） is triangle-equivalent to the stable category GF∩C of the Frobenius category of all Gorenstein fiat and cotorsion left R-modules.
基金partially supported by the NSFC(Nos.11722101,11871282,11931007)BNSF(Z190003)+1 种基金Nankai Zhide FoundationBeijing Institute of Technology Research Fund Program for Young Scholars.
文摘An isoparametric family in the unit sphere consists of parallel isoparametric hypersurfaces and their two focal submanifolds.The present paper has two parts.The first part investigates topology of the isoparametric families,namely the homotopy,homeomorphism,or diffeomorphism types,parallelizability,as well as the Lusternik-Schnirelmann category.This part extends substantially the results of Wang(J Differ Geom 27:55-66,1988).The second part is concerned with their curvatures;more precisely,we determine when they have non-negative sectional curvatures or positive Ricci curvatures with the induced metric.
文摘In this paper, we study the homotopy category of unbounded complexes of strongly copure projective modules with bounded relative homologies K;（SCP）.We show that the existence of a right recollement of K;（SCP） with respect to K;（SCP）, K;（SCP） and K;（SCP） has the homotopy category of strongly copure projective acyclic complexes as a triangulated subcategory in some case.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11522113 and 11571329)Australian Research Council grant DP160101481
文摘By assigning to each complex over a semi-simple ring two acyclicizations, we construct an explicit recollement for homotopy categories of a certain triangular matrix ring such that all the six triangle functors of the recollement preserve acyclic complexes.
基金the National Natural Science Foundation of China(Nos.11522113,11571329)。
文摘For an upper triangular matrix ring, an explicit ladder of height 2 of triangle functors between homotopy categories is constructed. Under certain conditions, the author obtains a localization sequence of homotopy categories of acyclic complexes of injective modules.
基金Supported by National Natural Science Foundation of China
文摘K. A. Hardie and K. H. Kamps investigated the track homotopy category H_B over a fixed space B ([1]). They have introduced two pairs of adjoint functors: P_B -|N_B and m_* -| m~*, where P_B:H_B→H^B, and m_*:H_A→H_B for a fixed map m: A→B. We have introduced a split fibration of categories L: H_b→H_B and proved L-|J, J-|L in [2]. This paper first extends P_B-|N_B to P_b_*-|N_Bb~# for any fixed map b:B→.Moreover we also extend these results to obtain two pairs of adjoint functors involving track homotopy categories H_b and H^b where H^b is the dual of H_b. One of our results is N_b-|P_b. This differs from P_B-|N_B.
