I am a beginner in Algebraic Topology and Differential Topology. Please suggest me a reference book to study Thom-Pontryagin Theory from basic and which book is easy to understand for a beginner. Thank you.
2026-05-16 12:19:40.1778933980
A reference book to study Thom-Pontryagin Theory from basic
105 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in ALGEBRAIC-TOPOLOGY
- How to compute homology group of $S^1 \times S^n$
- the degree of a map from $S^2$ to $S^2$
- Show $f$ and $g$ are both homeomorphism mapping of $T^2$ but $f$ is not homotopy equivalent with $g.$
- Chain homotopy on linear chains: confusion from Hatcher's book
- Compute Thom and Euler class
- Are these cycles boundaries?
- a problem related with path lifting property
- Bott and Tu exercise 6.5 - Reducing the structure group of a vector bundle to $O(n)$
- Cohomology groups of a torus minus a finite number of disjoint open disks
- CW-structure on $S^n$ and orientations
Related Questions in MANIFOLDS
- a problem related with path lifting property
- Levi-Civita-connection of an embedded submanifold is induced by the orthogonal projection of the Levi-Civita-connection of the original manifold
- Possible condition on locally Euclidean subsets of Euclidean space to be embedded submanifold
- Using the calculus of one forms prove this identity
- "Defining a smooth structure on a topological manifold with boundary"
- On the differentiable manifold definition given by Serge Lang
- Equivalence of different "balls" in Riemannian manifold.
- Hyperboloid is a manifold
- Integration of one-form
- The graph of a smooth map is a manifold
Related Questions in DIFFERENTIAL-TOPOLOGY
- Getting a self-homeomorphism of the cylinder from a self-homeomorphism of the circle
- what is Sierpiński topology?
- Bott and Tu exercise 6.5 - Reducing the structure group of a vector bundle to $O(n)$
- The regularity of intersection of a minimal surface and a surface of positive mean curvature?
- What's the regularity of the level set of a ''semi-nondegenerate" smooth function on closed manifold?
- Help me to prove related path component and open ball
- Poincarè duals in complex projective space and homotopy
- Hyperboloid is a manifold
- The graph of a smooth map is a manifold
- Prove that the sets in $\mathbb{R}^n$ which are both open and closed are $\emptyset$ and $\mathbb{R}^n$
Related Questions in SMOOTH-MANIFOLDS
- Smooth Principal Bundle from continuous transition functions?
- Possible condition on locally Euclidean subsets of Euclidean space to be embedded submanifold
- "Defining a smooth structure on a topological manifold with boundary"
- Hyperboloid is a manifold
- The graph of a smooth map is a manifold
- A finite group G acts freely on a simply connected manifold M
- An elementary proof that low rank maps cannot be open
- What does it mean by standard coordinates on $R^n$
- Partial Differential Equation using theory of manifolds
- Showing that a diffeomorphism preserves the boundary
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
geometry
circles
algebraic-number-theory
functions
real-analysis
elementary-set-theory
proof-verification
proof-writing
number-theory
elementary-number-theory
puzzle
game-theory
calculus
multivariable-calculus
partial-derivative
complex-analysis
logic
set-theory
second-order-logic
homotopy-theory
winding-number
ordinary-differential-equations
numerical-methods
derivatives
integration
definite-integrals
probability
limits
sequences-and-series
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
The standard reference for this would be Robert Stong's book "Notes on Cobordism Theory". The first chapter sets up the theory of cobordism categories, and then in the second chapter, the Pontryagin-Thom Theorem is proved in the generality of cobordism classes of manifolds with normal/tangential structure. I think this book is not too difficult to understand. Nonetheless, the first chapter requires some basic category theory.