A chain complex for the spectrum homology of the algebraic K-theory of an exact category

1997 ◽  
pp. 199-220 ◽  
Author(s):  
Randolph McCarthy
Keyword(s):  
Chain Complex ◽  
Exact Category ◽  
K Theory ◽  
A Chain

scholarly journals AN INVARIANT OF LEGENDRIAN AND TRANSVERSE LINKS FROM OPEN BOOK DECOMPOSITIONS OF CONTACT 3-MANIFOLDS

2020 ◽  
pp. 1-33
Author(s):  
ALBERTO CAVALLO
Keyword(s):  
Chain Complex ◽  
Open Book ◽  
Rational Homology ◽  
Open Book Decompositions ◽  
Chain Complexes ◽  
Legendrian Links ◽  
Sum Formula ◽  
A Chain ◽  
Special Cycle ◽  
Rational Homology Sphere

Abstract We introduce a generalization of the Lisca–Ozsváth–Stipsicz–Szabó Legendrian invariant ${\mathfrak L}$ to links in every rational homology sphere, using the collapsed version of link Floer homology. We represent a Legendrian link L in a contact 3-manifold ${(M,\xi)}$ with a diagram D, given by an open book decomposition of ${(M,\xi)}$ adapted to L, and we construct a chain complex ${cCFL^-(D)}$ with a special cycle in it denoted by ${\mathfrak L(D)}$ . Then, given two diagrams ${D_1}$ and ${D_2}$ which represent Legendrian isotopic links, we prove that there is a map between the corresponding chain complexes that induces an isomorphism in homology and sends ${\mathfrak L(D_1)}$ into ${\mathfrak L(D_2)}$ . Moreover, a connected sum formula is also proved and we use it to give some applications about non-loose Legendrian links; that are links such that the restriction of ${\xi}$ on their complement is tight.

scholarly journals Synthesis, Crystal Structure, and N2-Adsorption Property of a Chain Complex of Rhodium(II) Benzoate and Piperazine

2013 ◽  
Vol 29 (0) ◽  
pp. 21-22 ◽  
Author(s):  
Masahiro MIKURIYA ◽  
Kazuya OUCHI ◽  
Yasutaka NAKANISHI ◽  
Daisuke YOSHIOKA ◽  
Hidekazu TANAKA ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Adsorption Property ◽  
Chain Complex ◽  
N2 Adsorption ◽  
A Chain

scholarly journals CATEGORIFICATION OF THE DICHROMATIC POLYNOMIAL FOR GRAPHS

2008 ◽  
Vol 17 (01) ◽  
pp. 31-45 ◽  
Author(s):  
MARKO STOŠIĆ
Keyword(s):  
Positive Integer ◽  
Euler Characteristic ◽  
Jones Polynomial ◽  
Chain Complex ◽  
Tutte Polynomial ◽  
A Chain ◽  
Alternating Link ◽  
Dichromatic Polynomial

For each graph and each positive integer n, we define a chain complex whose graded Euler characteristic is equal to an appropriate n-specialization of the dichromatic polynomial. This also gives a categorification of n-specializations of the Tutte polynomial of graphs. Also, for each graph and integer n ≤ 2, we define the different one-variable n-specializations of the dichromatic polynomial, and for each polynomial, we define graded chain complex whose graded Euler characteristic is equal to that polynomial. Furthermore, we explicitly categorify the specialization of the Tutte polynomial for graphs which corresponds to the Jones polynomial of the appropriate alternating link.

scholarly journals Title: Supercomplex formed by the cross-binding of multiple antibody-single repeat chain complex gives signal amplification of antibody based assay

2021 ◽  
Author(s):  
Yongchan Lee ◽  
SunMin Kim ◽  
Jongchan Park ◽  
MuHyeon Choe
Keyword(s):  
Background Noise ◽  
Signal Amplification ◽  
Chain Complex ◽  
Antibody Binding ◽  
Binding Domain ◽  
Assay Method ◽  
Sensitive Assay ◽  
The Cross ◽  
Immunological Assays ◽  
A Chain

Abstract It is a challenging subject of biomedical research to develop more efficient and sensitive assay method. New method for enhancing sensitivity and precision of conventional immunological assays is developed. The antibody binding domain of Streptococcus protein G was used to make a chain of repeated antibody binding domain. The repeat chain was mixed with antibody, and multiple number of antibody bound to the repeat chain to form multiple antibody-repeat chain complex. The cross-binding between the complexes formed supercomplex, and the supercomplex amplified signals without specificity loss and background noise increase.

On Küneth’s correlation and its applications

2019 ◽  
Vol 26 (2) ◽  
pp. 295-301
Author(s):  
Leonard Mdzinarishvili
Keyword(s):  
Exact Sequence ◽  
Hausdorff Space ◽  
Chain Complex ◽  
Abelian Category ◽  
Derived Functor ◽  
Direct System ◽  
Arbitrary Complex ◽  
Formula Group ◽  
Čech Homology ◽  
A Chain

Abstract Let {\mathcal{K}} be an abelian category that has enough injective objects, let {T\colon\mathcal{K}\to A} be any left exact covariant additive functor to an abelian category A and let {T^{(i)}} be a right derived functor, {u\geq 1} , [S. Mardešić, Strong Shape and Homology, Springer Monogr. Math., Springer, Berlin, 2000]. If {T^{(i)}=0} for {i\geq 2} and {T^{(i)}C_{n}=0} for all {n\in\mathbb{Z}} , then there is an exact sequence 0\longrightarrow T^{(1)}H_{n+1}(C_{*})\longrightarrow H_{n}(TC_{*})% \longrightarrow TH_{n}(C_{*})\longrightarrow 0, where {C_{*}=\{C_{n}\}} is a chain complex in the category {\mathcal{K}} , {H_{n}(C_{*})} is the homology of the chain complex {C_{*}} , {TC_{*}} is a chain complex in the category A, and {H_{n}(TC_{*})} is the homology of the chain complex {TC_{*}} . This exact sequence is the well known Künneth’s correlation. In the present paper Künneth’s correlation is generalized. Namely, the conditions are found under which the infinite exact sequence \displaystyle\cdots\longrightarrow T^{(2i+1)}H_{n+i+1}\longrightarrow\cdots% \longrightarrow T^{(3)}H_{n+2}\longrightarrow T^{(1)}H_{n+1}\longrightarrow H_% {n}(TC_{*}) \displaystyle\longrightarrow TH_{n}(C_{*})\longrightarrow T^{(2)}H_{n+1}% \longrightarrow T^{(4)}H_{n+2}\longrightarrow\cdots\longrightarrow T^{(2i)}H_{% n+i}\longrightarrow\cdots holds, where {T^{(2i+1)}H_{n+i+1}=T^{(2i+1)}H_{n+i+1}(C_{*})} , {T^{(2i)}H_{n+i}=T^{(2i)}H_{n+i}(C_{*})} . The formula makes it possible to generalize Milnor’s formula for the cohomologies of an arbitrary complex, relatively to the Kolmogorov homology to the Alexandroff–Čech homology for a compact space, to a generative result of Massey for a local compact Hausdorff space X and a direct system {\{U\}} of open subsets U of X such that {\overline{U}} is a compact subset of X.

K-theory of n-coherent rings

2021 ◽  
pp. 2350007
Author(s):  
Eugenia Ellis ◽  
Rafael Parra
Keyword(s):  
Full Subcategory ◽  
Projective Dimension ◽  
Exact Category ◽  
Finite Projective Dimension ◽  
Coherent Ring ◽  
K Theory ◽  
Coherent Rings

Let [Formula: see text] be a strong [Formula: see text]-coherent ring such that each finitely [Formula: see text]-presented [Formula: see text]-module has finite projective dimension. We consider [Formula: see text] the full subcategory of [Formula: see text]-Mod of finitely [Formula: see text]-presented modules. We prove that [Formula: see text] is an exact category, [Formula: see text] for every [Formula: see text] and we obtain an expression of [Formula: see text].

scholarly journals A chain complex and quadrilaterals for normal surfaces

2013 ◽  
Vol 43 (2) ◽  
pp. 479-487
Author(s):  
Siddhartha Gadgil ◽  
Tejas Kalelkar
Keyword(s):  
Chain Complex ◽  
Normal Surfaces ◽  
A Chain

scholarly journals Synthesis and Crystal Structure of a Chain Complex of Molybdenum(II) Benzoate and 1,2-Bis(4-pyridyl)ethane with an N2-Adsorption Property

2014 ◽  
Vol 30 (0) ◽  
pp. 39-40 ◽  
Author(s):  
Masahiro MIKURIYA ◽  
Noriaki KAIHARA ◽  
Takashi ONO ◽  
Yusuke TANAKA ◽  
Daisuke YOSHIOKA ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Adsorption Property ◽  
Chain Complex ◽  
N2 Adsorption ◽  
Synthesis And Crystal Structure ◽  
A Chain
Sign in / Sign up

Export Citation Format

Share Document