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### A Certain Exact Sequence

theorems concern, first of all, an exact sequence, 2(K), where K is a ... J. H. C.WHITEHEAD, On the realizability of homotopy groups,Ann. of Math., ...
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### Intuitive Meaning Of Exact Sequence - Mathematics Stack Exchange

Jun 13, 2013 ... Some standard exact sequences · 0→Aa→B is exact iff a is 1-1. · Bb→C→0 is exact iff b is onto. · If Aa→Bb→C→0 and 0→Cc→Dd→E are exact, ...
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### Hopf Bimodules, Coquasibialgebras, And An Exact Sequence Of Kac ...

Based on the ideas of Tannaka–Kreın reconstruction, we present a categorical construction that assigns to any cleft Hopf algebra inclusion K⊂H a coqua… Feb 10, 2002 ... Advances in Mathematics ... Hopf Bimodules, Coquasibialgebras, and an Exact Sequence of Kac☆ ... Pacific J. Math., 137 (1989), pp. 37-54.
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### Lim^1 And Milnor Sequences

Such a situation is expressed by a short exact Milnor sequence (below). ... John Milnor, On axiomatic homology theory, Pacific J. Math.
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### What Is A Short Exact Sequence Telling Me? - Mathematics Stack ...

Jul 11, 2014 ... As a big picture thing, a short exact sequences are essentially arithmetic calculations where you're doing arithmetic with groups (and ...
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### The Birman Exact Sequence Does Not Virtually Split

This paper answers a basic question about the Birman exact sequence in the
theory of mapping class groups. We prove that the Birman exact sequence does
not admit a section over any subgroup $Γ$ contained in the Torelli group
with finite index. A fortiori this proves that there is no section of the
Birman exact sequence for any finite-index subgroup of the full mapping class
group. This theorem was announced in a 1990 preprint of G. Mess, but an error
was uncovered and described in a recent paper of the first author. Mathematics > Geometric Topology. arXiv:1804.11235 (math). [Submitted on 30 Apr 2018]. Title:The Birman exact sequence does not virtually split.
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### A Systematic Construction Of Finite Element Commuting Exact ...

We present a systematic construction of finite element exact sequences with a commuting diagram property for the de Rham complex in one-, two-, and three-space dimensions. We apply the construction in two-space dimensions to rediscover two families of exact sequences for triangles and three for squares, and to uncover one new family of exact sequence for squares and two new families of exact sequences for general polygonal elements. We apply the construction in three-space dimensions to rediscover two families of exact sequences for tetrahedra, three for cubes, and one for prisms, and to uncover four new families of exact sequences for pyramids, three for prisms, and one for cubes. We present a systematic construction of finite element exact sequences with a commuting diagram property for the de Rham complex in one-, two-, ...
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### AN INTRODUCTION TO SPECTRAL SEQUENCES 1. Example We ...

THE INFLATION-RESTRICTION SEQUENCE : AN INTRODUCTION TO SPECTRAL SEQUENCES. TOM WESTON. 1. Example. We begin with abelian groups E.
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### Math 751 Notes Week 10

Take the associated long exact sequence for homology. We next discuss chain maps induced by maps of pairs of spaces. Let f : (X, A) → (Y,B) be ...
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### SPLITTING OF SHORT EXACT SEQUENCES FOR GROUPS 1 ...

cal algebra (the type of algebra underlying algebraic topology) spread exact sequences into the rest of mathematics. Example 1.1. The determinant on GL2(R) ...
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### Exact Sequence - Encyclopedia Of Mathematics

Jun 5, 2020 ... An exact sequence 0→A→B→C→0 is called short, and consists of an object B, a subobject A of it and the corresponding quotient object C.
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