In the mathematical surgery theory the surgery exact sequence is the main technical tool to calculate the surgery structure set of a compact manifold in dimension . The surgery structure set of a compact -dimensional manifold is a pointed set which classifies -dimensional manifolds within the homotopy type of . The basic idea is that in order to calculate it is enough to understand the other terms in the sequence, which are usually easier to determine. These are on one hand the normal invariants which form generalized cohomology groups, and hence one can use standard tools of algebraic topology to calculate them at least in principle. On the other hand, there are the L-groups which are defined algebraically in terms of quadratic forms or in terms of chain complexes with quadratic structure. A great deal is known about these groups. Another part of the sequence are the surgery obstruction maps from normal invariants to the L-groups. For these maps there are certain characteristic classes formulas, which enable to calculate them in some cases. Knowledge of these three components, that means: the normal maps, the L-groups and the surgery obstruction maps is enough to determine the structure set (at least up to extension problems). In practice one has to proceed case by case, for each manifold it is a unique task to determine the surgery exact sequence, see some examples below. Also note that there are versions of the surgery exact sequence depending on the category of manifolds we work with: smooth (DIFF), PL, or topological manifolds and whether we take Whitehead torsion into account or not (decorations or ). The original 1962 work of Browder and Novikov on the existence and uniqueness of manifolds within a simply-connected homotopy type was reformulated by Sullivan in 1966 as a surgery exact sequence.In 1970 Wall developed non-simply-connected surgery theory and the surgery exact sequence for manifolds with arbitrary fundamental group. (Wikipedia).
What is the definition of a geometric sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
What is the alternate in sign sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
What is an arithmetic sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
Dehn Twists Exact Sequences Through Lagrangian Cobordism - Weiwei Wu
Weiwei Wu University of Montreal October 23, 2015 https://www.math.ias.edu/seminars/abstract?event=85044 In this talk we first introduce a new "singularity-free" approach to the proof of Seidel's long exact sequence, including the fixed-point version. This conveniently generalizes to Deh
From playlist PU/IAS Symplectic Geometry Seminar
Paolo Piazza: Surgery sequences and higher invariants of Dirac operators
Talk by Paolo Piazza in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on March 10, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
Learn how to determine if a sequence is an example of an arithmetic sequence or not
👉 Learn how to determine if a sequence is arithmetic, geometric, or neither. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric seque
From playlist Sequences
What is the definition of an arithmetic sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
Markus Land - L-Theory of rings via higher categories II
For questions and discussions of the lecture please go to our discussion forum: https://www.uni-muenster.de/TopologyQA/index.php?qa=k%26l-conference This lecture is part of the event "New perspectives on K- and L-theory", 21-25 September 2020, hosted by Mathematics Münster: https://go.wwu
From playlist New perspectives on K- and L-theory
Erik Kjær Pedersen: Some remarks on the surgery exact sequence
The lecture was held within the framework of the Hausdorff Trimester Program: K-theory in topology and non commutative geometry.
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Christoph Winges: Automorphisms of manifolds and the Farrell Jones conjectures
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Building on previous work of Bartels, Lück, Reich and others studying the algebraic K-theory and L-theory of discrete group rings, the validity of the Farrell-Jones Conjecture has be
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
Mladen Bestvina: The Farrell-Jones conjecture for free-by-cyclic groups
Abstract: The Farrell-Jones conjecture for a given group is an important conjecture in manifold theory. I will review some of its consequences and will discuss a class of groups for which it is known, for example 3-manifold groups. Finally, I will discuss a proof that free-by-cyclic groups
From playlist Topology
Fukaya category for Landau-Ginzburg orbifolds and Berglund-Hübsch homological...- Cheol-Hyun Cho
IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Topic: Fukaya category for Landau-Ginzburg orbifolds and Berglund-Hübsch homological mirror symmetry for curve singularities Speaker: Cheol-Hyun Cho Affiliation: Seoul National University Date: September 21, 2020 For more video please vi
From playlist Mathematics
Introduction to Sequences (Discrete Math)
This video introduces sequences for a discrete math class. mathispower4u.com
From playlist Sequences (Discrete Math)
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
Non-standard Contact Structures on Spheres and Applications - Agustin Moreno
Special Joint IAS/Princeton University Symplectic Geometry Seminar Topic: Non-standard Contact Structures on Spheres and Applications Speaker: Agustin Moreno Affiliation: Member, School of Mathematics Date: February 13, 2023 In this talk, I will describe the construction of contact struc
From playlist Mathematics
How to determine if an sequence is arithmetic or not
👉 Learn how to determine if a sequence is arithmetic, geometric, or neither. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric seque
From playlist Sequences
Determine if a sequence is geometric or not
👉 Learn how to determine if a sequence is arithmetic, geometric, or neither. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric seque
From playlist Sequences
Determine if a sequence is geometric or not
👉 Learn how to determine if a sequence is arithmetic, geometric, or neither. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric seque
From playlist Sequences