The authors consider the difference of Reidemeister traces and difference cochain of given two self-maps, and find out a relation involving these two invariants.As an application, an inductive formula of the Reidemeis...The authors consider the difference of Reidemeister traces and difference cochain of given two self-maps, and find out a relation involving these two invariants.As an application, an inductive formula of the Reidemeister traces for self-maps on a kind of CW-complex, including spherical manifolds is obtained.展开更多
The main objective of this paper is to provide the tool rather than the classical adjoint representation of Lie algebra;which is essential in the conception of the Chevalley Eilenberg Cohomology. We introduce the noti...The main objective of this paper is to provide the tool rather than the classical adjoint representation of Lie algebra;which is essential in the conception of the Chevalley Eilenberg Cohomology. We introduce the notion of representation induced by a 2 - 3 matrix. We construct the corresponding Chevalley Eilenberg differential and we compute all its cohomological groups.展开更多
We show that a Lipschitz domain can be expanded solely near a part of its boundary, assuming that the part is enclosed by a piecewise C1 curve. The expanded domain as well as the extended part are both Lipschitz. We a...We show that a Lipschitz domain can be expanded solely near a part of its boundary, assuming that the part is enclosed by a piecewise C1 curve. The expanded domain as well as the extended part are both Lipschitz. We apply this result to prove a regular decomposition of standard wector Sobolev spaces with vanishing traces only on part of the boundary. Another application in the construction of low-regularity projectors into finite element spaces with partial boundary conditions is also indicated.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11431009,11661131004)
文摘The authors consider the difference of Reidemeister traces and difference cochain of given two self-maps, and find out a relation involving these two invariants.As an application, an inductive formula of the Reidemeister traces for self-maps on a kind of CW-complex, including spherical manifolds is obtained.
文摘The main objective of this paper is to provide the tool rather than the classical adjoint representation of Lie algebra;which is essential in the conception of the Chevalley Eilenberg Cohomology. We introduce the notion of representation induced by a 2 - 3 matrix. We construct the corresponding Chevalley Eilenberg differential and we compute all its cohomological groups.
文摘We show that a Lipschitz domain can be expanded solely near a part of its boundary, assuming that the part is enclosed by a piecewise C1 curve. The expanded domain as well as the extended part are both Lipschitz. We apply this result to prove a regular decomposition of standard wector Sobolev spaces with vanishing traces only on part of the boundary. Another application in the construction of low-regularity projectors into finite element spaces with partial boundary conditions is also indicated.
