1. notice
  3. English
  5. logic-topic
  6. 1. logic
  7. 2. basic
  8. 3. map
  9. 4. order
  10. 5. combinatorics
  12. calculus
  13. 6. real-numbers
  14. 7. limit-sequence
  15. 8. division-algebra
  16. 9. Euclidean-space
  17. 10. Minkowski-space
  18. 11. polynomial
  19. 12. analytic-Euclidean
  20. 13. analytic-struct-operation
  21. 14. ordinary-differential-equation
  22. 15. volume
  23. 16. integral
  24. 17. divergence
  25. 18. limit-net
  26. 19. topology
  27. 20. compact
  28. 21. connected
  29. 22. topology-struct-operation
  30. 23. exponential
  31. 24. angle
  33. geometry
  34. 25. manifold
  35. 26. metric
  36. 27. metric-connection
  37. 28. geodesic-derivative
  38. 29. curvature-of-metric
  39. 30. Einstein-metric
  40. 31. constant-sectional-curvature
  41. 32. simple-symmetric-space
  42. 33. principal-bundle
  43. 34. group
  44. 35. stereographic-projection
  45. 36. Hopf-bundle
  47. field-theory
  48. 37. point-particle-non-relativity
  49. 38. point-particle-relativity
  50. 39. scalar-field
  51. 40. scalar-field-current
  52. 41. scalar-field-non-relativity
  53. 42. projective-lightcone
  54. 43. spacetime-momentum-spinor-representation
  55. 44. Lorentz-group
  56. 45. spinor-field
  57. 46. spinor-field-current
  58. 47. electromagnetic-field
  59. 48. Laplacian-of-tensor-field
  60. 49. Einstein-metric
  61. 50. interaction
  62. 51. harmonic-oscillator-quantization
  63. 52. spinor-field-misc
  64. 53. reference
  66. ไธญๆ–‡
  67. 54. notice
  69. ้€ป่พ‘
  70. 55. ้€ป่พ‘
  71. 56. ๅŸบ็ก€
  72. 57. ๆ˜ ๅฐ„
  73. 58. ๅบ
  74. 59. ็ป„ๅˆ
  76. ๅพฎ็งฏๅˆ†
  77. 60. ๅฎžๆ•ฐ
  78. 61. ๆ•ฐๅˆ—ๆž้™
  79. 62. ๅฏ้™คไปฃๆ•ฐ
  80. 63. Euclidean ็ฉบ้—ด
  81. 64. Minkowski ็ฉบ้—ด
  82. 65. ๅคš้กนๅผ
  83. 66. ่งฃๆž (Euclidean)
  84. 67. ่งฃๆž struct ็š„ๆ“ไฝœ
  85. 68. ๅธธๅพฎๅˆ†ๆ–น็จ‹
  86. 69. ไฝ“็งฏ
  87. 70. ็งฏๅˆ†
  88. 71. ๆ•ฃๅบฆ
  89. 72. ็ฝ‘ๆž้™
  90. 73. ๆ‹“ๆ‰‘
  91. 74. ็ดง่‡ด
  92. 75. ่ฟž้€š
  93. 76. ๆ‹“ๆ‰‘ struct ็š„ๆ“ไฝœ
  94. 77. ๆŒ‡ๆ•ฐๅ‡ฝๆ•ฐ
  95. 78. ่ง’ๅบฆ
  97. ๅ‡ ไฝ•
  98. 79. ๆตๅฝข
  99. 80. ๅบฆ่ง„
  100. 81. ๅบฆ่ง„็š„่”็ปœ
  101. 82. Levi-Civita ๅฏผๆ•ฐ
  102. 83. ๅบฆ่ง„็š„ๆ›ฒ็Ž‡
  103. 84. Einstein ๅบฆ่ง„
  104. 85. ๅธธๆˆช้ขๆ›ฒ็Ž‡
  105. 86. simple-symmetric-space
  106. 87. ไธปไธ›
  107. 88. ็พค
  108. 89. ็ƒๆžๆŠ•ๅฝฑ
  109. 90. Hopf ไธ›
  111. ๅœบ่ฎบ
  112. 91. ้ž็›ธๅฏน่ฎบ็‚น็ฒ’ๅญ
  113. 92. ็›ธๅฏน่ฎบ็‚น็ฒ’ๅญ
  114. 93. ็บฏ้‡ๅœบ
  115. 94. ็บฏ้‡ๅœบ็š„ๅฎˆๆ’ๆต
  116. 95. ้ž็›ธๅฏน่ฎบ็บฏ้‡ๅœบ
  117. 96. ๅ…‰้”ฅๅฐ„ๅฝฑ
  118. 97. ๆ—ถ็ฉบๅŠจ้‡็š„่‡ชๆ—‹่กจ็คบ
  119. 98. Lorentz ็พค
  120. 99. ๆ—‹้‡ๅœบ
  121. 100. ๆ—‹้‡ๅœบ็š„ๅฎˆๆ’ๆต
  122. 101. ็”ต็ฃๅœบ
  123. 102. ๅผ ้‡ๅœบ็š„ Laplacian
  124. 103. Einstein ๅบฆ่ง„
  125. 104. ็›ธไบ’ไฝœ็”จ
  126. 105. ่ฐๆŒฏๅญ้‡ๅญๅŒ–
  127. 106. ๆ—‹้‡ๅœบๆ‚้กน
  128. 107. ๅ‚่€ƒ

note-math

At first glance, the quotient of Euclidean projective space seems trivial, but once generalized to complex quaternions, the seemingly non-trivial Hopf bundle, a type of fiber bundle, appears. The real case is the bundle. The case of the quaternion Hopf bundle may also be related to the construction of exotic .

or complex number version of Hopf-bundle

[Hopf-bundle]

Embedding , in use as stereographic-projection coordinates

The transformation function of the two coordinates of stereographic projection or

does not change the projective result e.g.

is a bundle on

Construct bundle coordinates with two stereographic projection coordinates

and

And the transformation function or

You can first quotient

At this point, the representation of stereographic projection

does not change the projective result

is a bundle on

Construct bundle coordinates with two stereographic projection coordinates

and

And the transformation function or