Notes on Chain Complexes

نویسنده

  • ANDREW BAKER
چکیده

These notes are intended as a very basic introduction to (co)chain complexes and their algebra, the intention being to point the beginner at some of the main ideas which should be further studied by in depth reading. An accessible introduction for the beginner is [2]. An excellent modern reference is [3], while [1] is a classic but likely to prove hard going for a novice. Most introductory books on algebraic topology introduce the language and basic ideas of homological algebra.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Polytopal complexes: maps, chain complexes and... necklaces

The notion of polytopal map between two polytopal complexes is defined. Surprisingly, this definition is quite simple and extends naturally those of simplicial and cubical maps. It is then possible to define an induced chain map between the associated chain complexes. Finally, we use this new tool to give the first combinatorial proof of the splitting necklace theorem of Alon. The paper ends wi...

متن کامل

Group (IV) Metallocene Complexes with Bulky ω-aryloxyalkyl-Substituted Indenyl Ligands as Catalyst Precursors for Homogeneous Ethylene Polymerization

 A series of seven new complexes of zirconium and hafnium with bulky ω-aryloxyalkyl substituted indenyl ligands were synthesized and characterized by NMR spectroscopy and elemental analysis. These complexes were activated with methylaluminoxane and tested for homogeneous ethylene polymerization. The zirconium catalysts showed higher activities than their hafnium an...

متن کامل

Long-term, high-dose aspirin therapy increases the specific activity of complex III of mitochondrial respiratory chain in the kidney of diabetic rats

Introduction: One of the main mechanisms by which diabetic complications occur is an alteration of the structure and function of proteins due to hyperglycemia. Aspirin (ASA) affects cellular pathways through different mechanisms, including glycation inhibition and antioxidant activity. The aim of the present study, as a follow up to our previous one, is to investigate the effect of long-term, h...

متن کامل

Notes on Tor and Ext

1. Basic homological algebra 1 1.1. Chain complexes 2 1.2. Maps and homotopies of maps of chain complexes 2 1.3. Tensor products of chain complexes 3 1.4. Short and long exact sequences 3 1.5. Dual cochain complexes and Hom complexes 4 1.6. Relations between ⊗ and Hom 4 2. The universal coefficient and Künneth theorems 5 2.1. Universal coefficients in homology 5 2.2. The Künneth theorem 6 2.3. ...

متن کامل

Second symmetric powers of chain complexes

We investigate Buchbaum and Eisenbud's construction of the second symmetric power $s_R(X)$ of a chain complex $X$ of modules over a commutative ring $R$. We state and prove a number of results from the folklore of the subject for which we know of no good direct references. We also provide several explicit computations and examples. We use this construction to prove the following vers...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009