Join experts in discussing differential geometry topics. This includes manifolds, Tensors and forms. Connections and curvature also. Differential and algebraic topology discussion.
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Graduate Proving Hopf Invariant and Degree of g for f⋅g
- eok20
- · Replies 2 ·
Undergrad Analytic Geometry - finding the normal vector at a point
- cfphys
- · Replies 3 ·
Graduate Is classical differential geometry still useful?
- petergreat
- · Replies 1 ·
Graduate Smoothness of the Reeb vector field of a contact form
- quasar987
- · Replies 11 ·
Graduate Definition of a homeomorphism between topological spaces
- RedX
- · Replies 10 ·
Graduate Intersection of Connected Sets: True or False?
- beetle2
- · Replies 7 ·
Graduate I have some trouble with the fourth spatial dimension
- TubbaBlubba
- · Replies 2 ·
Graduate Arc length parameter for u¹ curves and metric tensor g₁₁
- SNOOTCHIEBOOCHEE
- · Replies 1 ·
High School Area of standard-sized dartboard?
- moonman239
- · Replies 5 ·
Graduate Relationship between Diffeomorphism and Jacobian
- RedX
- · Replies 12 ·
High School What Defines a Straight Line?
- tauon
- · Replies 7 ·
Graduate Area of circle using incribed polygons
- Jamin2112
- · Replies 11 ·
Graduate Laplacian of 2-Form in R^3: Reference & Calculation
- haushofer
- · Replies 4 ·
Graduate Closure of a one-parameter subgroup
- eok20
- · Replies 1 ·
Graduate Conformally Flat and Einstein Geometry
- charlynd
- · Replies 4 ·
Graduate Equivalence Relations on [0,1]x[0,1] and Hausdorff Spaces
- lttlbbygurl
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Graduate Lie derivative versus covariant derivative
- RedX
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Graduate Are [-4,4] and (-3,3) open or closed in the topology τ = {∅} ∪ {u ⊆ ℝ : {-π,π} ⊆ u}?
- blbl
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Graduate Differentiable structures and diffeomorphisms
- RedX
- · Replies 5 ·
Graduate K-connectedness and the homotopy-lifting property
- Bacle
- · Replies 1 ·
Graduate How to prove these with Integral Theorems
- Gameowner
- · Replies 3 ·
Graduate Leray-Hirsch isomorphism and tensor product of cochain complexes
- Bacle
- · Replies 18 ·
Graduate Is the Continuum Hypothesis Valid if the Interval is Wrapped into a Semi-Circle?
- TheAlkemist
- · Replies 2 ·
Graduate Definition of boundary point and equation
- wayneckm
- · Replies 9 ·
Graduate Continuous bijection that is not an embedding
- Bacle
- · Replies 8 ·
Graduate What is the exterior derivative and how do you compute it?
- Terilien
- · Replies 18 ·
Graduate Why Does an Isometry Preserve Lie Brackets Between Vector Fields?
- rafax
- · Replies 1 ·
Graduate Proving the Inverse Function Theorem: A Struggle
- lttlbbygurl
- · Replies 1 ·
Graduate Why are the differentials dx^μ used as dual space bases?
- nklohit
- · Replies 8 ·
Graduate Residue calculus and gauss bonnet surfaces
- zwoodrow
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Graduate What Is a Quotient Bundle?
- Bacle
- · Replies 8 ·
Graduate Why is the iterated integral of two 1-forms homotopy invariant?
- lavinia
- · Replies 1 ·
Graduate Uniform continuity in top. spaces
- Bleys
- · Replies 5 ·
Graduate Request: Solved Problems in R.Geometry; Connections, etc.
- WWGD
- · Replies 3 ·
Graduate Lie algebra of the diffeomorphism group of a manifold.
- eok20
- · Replies 7 ·
Graduate Compute Euler Characteristic from Z Homology Dimensions
- lavinia
- · Replies 4 ·
Graduate Tangent map, gauss map, and shape operator
- badgers14
- · Replies 1 ·
Undergrad Postulates that Euclid neglected to mention?
- LeonhardEuler
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Graduate Are functionals united with the vector space which they operate on?
- jaketodd
- · Replies 9 ·
Graduate Is Parallel Transport Invariance Maintained in General Relativity Calculations?
- bueller11
- · Replies 10 ·
Graduate No difference between covectors and functions?
- mordechai9
- · Replies 4 ·
Graduate Exterior Derivative: Proving d^2 = 0 and d(w1 wedge w2) Properties
- jem05
- · Replies 6 ·
Graduate Global Section of Fiber Bundles with Contractible Fiber
- MagmaMorphic
- · Replies 2 ·
Graduate Fundamental group to second homology group
- lavinia
- · Replies 2 ·
Graduate Proof of Real Projective Plane Embedding in R4
- rainwyz0706
- · Replies 2 ·
Graduate Why does convergence in probability generate a topology but a.s. convergence does not?
- wayneckm
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Graduate Intro to elementary index notation
- fantispug
- · Replies 1 ·
Graduate Neumann boundary conditions on S^1/Z_2
- AntideSitter
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Graduate What is the concept of exact forms on a 2 torus and how can it be visualized?
- lavinia
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Graduate Math of Transfinite Donuts in 3-D Space
- HarryWertM
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Graduate What's the difference between differential topology and algebraic topology?
- petergreat
- · Replies 5 ·
Graduate Quotient Spaces/Homeomorphic spaces?
- sutupidmath
- · Replies 1 ·
Undergrad Graphing Surfaces with Non-Linear Equations: What Are My Options?
- aarciga
- · Replies 2 ·
Graduate Understanding Exterior Products of Multiple Vectors
- jostpuur
- · Replies 18 ·
Graduate Can a Symmetric Tensor on a Manifold of Signature -+++ be Written in p-forms?
- Phrak
- · Replies 8 ·
Graduate Cartan formalism for Christoffel symbols and curvature
- zwoodrow
- · Replies 2 ·
Graduate Learn Conical Coordinates with Mathworld
- TheDestroyer
- · Replies 3 ·
Graduate Fundamental group with n holes
- madness
- · Replies 8 ·
Graduate Proof of Homeomorphism: An Example
- beetle2
- · Replies 4 ·
Graduate Why Use 'Singular' to Describe Singular Simplex?
- navigator
- · Replies 3 ·
Graduate Fundamental Group of (X,p): D^2\{(x,0) : 0<=x<=1}
- Mikemaths
- · Replies 3 ·
Graduate Why aren't all closed loops at a point in the same homotopy class?
- Zetta
- · Replies 19 ·
Graduate Homotopy from a loop to a point in contractible domain
- Bacle
- · Replies 9 ·
Graduate Finite Complement Topology: Why It's the Finest
- beetle2
- · Replies 4 ·
Graduate What is the boundary of a surface?
- quasar987
- · Replies 15 ·
Graduate What Does the Homology Group Tell Us About a Manifold?
- Sumanta
- · Replies 4 ·
Graduate Generic Intersection of non-planar Surfaces in R^4
- Bacle
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Graduate What is the role of the transpose matrix in tensor transformations?
- peterjaybee
- · Replies 8 ·
Undergrad Why Use Open and Closed Sets in Mathematical Proofs?
- wayneckm
- · Replies 8 ·
Graduate Homology of CP^1, complex projective 1-space
- Bacle
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Graduate Relation between Frenet-Serret torsion and the torsion tensor?
- lucyk
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Graduate Levi-civita connection assumptions
- RedX
- · Replies 1 ·
Graduate Identifying tiles in hyperbolic space?
- Coin
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Graduate For M a 4-mfld., every class in H_2(M;Z) can be represented by a Surface.
- Bacle
- · Replies 13 ·
Undergrad Tangent and normal vectors at a point on a circle through three points
- CosmicVoyager
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Graduate Shortest arc between two points in polar coordinates
- mnb96
- · Replies 5 ·
Graduate Geometric description of (simplicial)homologous cycles
- Bacle
- · Replies 6 ·
Graduate Orientability of Complex Manifolds.
- Bacle
- · Replies 6 ·
Graduate What is the difference between a manifold and a metric space?
- RedX
- · Replies 24 ·
Graduate An intuitive explanation to the Killing equation?
- kvf
- · Replies 2 ·
Graduate Can a disconnected space be a disjoint union of two infinite sets?
- Mikemaths
- · Replies 5 ·
Graduate Need assistance,can you imagine a continuously deformation between X and Y?
- kakarotyjn
- · Replies 1 ·
Undergrad Hyperbolic Geometry: Euclidean v 4D in 3D Space
- Praxisseiz
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Graduate How to make curved line into torus?
- CosmicVoyager
- · Replies 1 ·
Graduate Represntative Surfaces/Curves in homology. Examples.?
- Bacle
- · Replies 7 ·
Graduate Good resources for symplectic manifold theorems easier than Arnold
- Nusc
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Graduate Why is a contractible space simply connected if path connectedness suffices?
- madness
- · Replies 11 ·
Graduate Is the square root loop from S^1 to RP^1 really a homeomorphism?
- madness
- · Replies 5 ·
Graduate Sphere as an embedded submanifold
- jem05
- · Replies 6 ·
Undergrad Definition of a line between two points on a sphere
- TravelGirl
- · Replies 13 ·
High School Definition of the Cross Product?
- 2^Oscar
- · Replies 11 ·
Undergrad How Does Horizontal Deviation Affect Elliptical Projection of a Sphere?
- Chandi
- · Replies 1 ·
Undergrad How Can You Calculate the Distance Between Two Pulley Centers Using Belt Length?
- itchy8me
- · Replies 18 ·
Graduate Is it possible to prove that any metric topology is Hausdorff?
- sutupidmath
- · Replies 4 ·
Graduate Proving curl(∇v)ᵀ = 0 using indicial notation
- traianus
- · Replies 15 ·
Graduate Can you compute Lie derivatives of tensors as commutators?
- linford86
- · Replies 8 ·
Graduate Contraction map of geometric mean
- rubinj
- · Replies 2 ·
Graduate Number of independent subcubes of a hypercube
- twoflower
- · Replies 1 ·
Graduate Translation in Spherical Coordinates
- karanmohan
- · Replies 1 ·
Graduate Can a Metric be Defined to Make All Balls in R^2 Unbounded with Shrinking Radii?
- jostpuur
- · Replies 7 ·