I am studying algebraic topology at the moment and I'm halfway done with Hatcher's book. I am extremely interested in low-dimensional topology, so I was wondering if anybody knows a good set of notes in knot theory and 4-dimensional manifolds. So any reference would be much appreciated
2026-03-25 14:20:12.1774448412
Notes on Low-Dimensional Topology
382 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in GENERAL-TOPOLOGY
- Is every non-locally compact metric space totally disconnected?
- Let X be a topological space and let A be a subset of X
- Continuity, preimage of an open set of $\mathbb R^2$
- Question on minimizing the infimum distance of a point from a non compact set
- Is hedgehog of countable spininess separable space?
- Nonclosed set in $ \mathbb{R}^2 $
- I cannot understand that $\mathfrak{O} := \{\{\}, \{1\}, \{1, 2\}, \{3\}, \{1, 3\}, \{1, 2, 3\}\}$ is a topology on the set $\{1, 2, 3\}$.
- If for every continuous function $\phi$, the function $\phi \circ f$ is continuous, then $f$ is continuous.
- Defining a homotopy on an annulus
- Triangle inequality for metric space where the metric is angles between vectors
Related Questions in REFERENCE-REQUEST
- Best book to study Lie group theory
- Alternative definition for characteristic foliation of a surface
- Transition from theory of PDEs to applied analysis and industrial problems and models with PDEs
- Random variables in integrals, how to analyze?
- Abstract Algebra Preparation
- Definition of matrix valued smooth function
- CLT for Martingales
- Almost locality of cubic spline interpolation
- Identify sequences from OEIS or the literature, or find examples of odd integers $n\geq 1$ satisfying these equations related to odd perfect numbers
- property of Lebesgue measure involving small intervals
Related Questions in KNOT-THEORY
- Is unknot a composite knot?
- Can we modify one component of a link and keep the others unchanged
- Can we split a splittable link by applying Reidemeister moves to non-self crossings only
- Involution of the 3 and 4-holed torus and its effects on some knots and links
- Equivalence polygonal knots with smooth knots
- Can a knot diagram be recovered from this data?
- Does Seifert's algorithm produce Seifert surfaces with minimal genus?
- Equivalence of links in $R^3$ or $S^3$
- Homotopy type of knot complements
- The complement of a knot is aspherical
Related Questions in LOW-DIMENSIONAL-TOPOLOGY
- Getting a self-homeomorphism of the cylinder from a self-homeomorphism of the circle
- Does $S^2\times[-1,1]$ decompose as $B^3\#B^3$
- Homologically zero circles in smooth manifolds
- Can we really move disks around a compact surface like this?
- Why is this not a valid proof of the Poincare Conjecture?
- Regarding Surgery and Orientation
- Can a one-dimensional shape have volume?
- The inside of a closed compact surface $\sum_g$
- How do you prove that this set is open?
- Understanding cobordisms constructed from a Heegaard triple
Related Questions in 4-MANIFOLDS
- Pontryagin class of self-dual forms on a 4-manifold
- Positive scalar curvature in dimension 4
- $S^6$ as the total space of bundle
- Area of Study for Four dimensional Space
- A Hodge dual computation on a $4$-dimensional Riemannian manifold
- notation for connected sum $\#^n S^2 \times S^2$
- How to think about exotic differentiable structures in manifolds?
- Twisty cross notation
- Examples of 4-manifolds with nontrivial third Stiefel-Whitney class $w_3$.
- About natural identifications in knot theory
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
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
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?
There are many introductory books on knot theory. I will list few in an order of increasing difficulty.
I haven't read Lickorish's book, so can't judge it. Material listed above should more than enough to understand fundamentals of knot theory. If you want to continue your journey with knots you should switch to reading papers from journals.