1. The first unstable homotopy group of $Sp(n)$
  2. Is there a relationship between a quotient group of the fundamental group of X and the fundamental group of a quotient topology of X?

  3. Homotopy invariant structure: Stasheff versus Segal
  4. Are there geometrically formal manifolds, which are not rationally elliptic?

  5. When is $max Spec R$ homotopy equivalent with $Spec R$ (with Zariski topology)?

  6. Is there a dense subset on closed Jordan curve $C$ which avoids intersections under certain rotations?

  7. Internal product on intersection (co)homology

  8. What do Atiyah and Segal mean by $K_G^*(X)$?
  9. Is there a geometric interpretation of a Zariski dense surface subgroup?

  10. No irreducible parallelizable manifold of a given dimension

  11. Compelling evidence that two basepoints are better than one
  12. Godbillon's proof of strong excision in de Rham cohomology with compact support
  13. Euler characteristic of a manifold and self-intersection

  14. $(\infty,2)$-Categorical Analogue of the Local Nature of Equivalences
  15. monadic decomposition
  16. Building conilpotent coalgebras from co-square-zero-extensions
  17. The Dold-Thom theorem for infinity categories?
  18. The Hopf invariant is an isomorphism for $\pi_3 (S^2)$
  19. One colored infinity operads via symmetric sequences?

  20. Reference request: cohomology of Eilenberg Maclane spaces with $p$-local groups
  21. When are the homology and cohomology Hopf algebras of topological groups equal?
  22. Why is the standard definition of cocycle the one that _always_ comes up??

  23. Tensor product of coaugmented conilpotent coalgebras

  24. SO(3) action on (simply connected) 6 manifold with discrete fixed point

  25. Stiefel-Whitney classes of tensor product $\xi^m \otimes \eta^n$, computation
  26. equivalence of Grothendieck-style versus Cech-style sheaf cohomology

  27. Equivariant handle decompositions

  28. triangulations of torus, general, and Euler number. (Hopefully more interesting/relevant)

  29. Direct proof of the equivalence of symmetric monoidal $K$-theory and exact sequence $K$-theory?

  30. Linking topological spheres
  31. What is a continuous path?

  32. Space of sections of a fibration under weak homotopy equivalence
  33. Can a PDE constrain the degree of a $C^\infty$ map germ?

  34. Is the projection $ f: S^2 \times S^3 \to S^2 $ cocyclic?

  35. A question on Grothendieck Riemann Roch
  36. Under what condition is a fiber bundle cobordant to the trivial bundle?

  37. Naturality of Moore-Postnikov systems

  38. Ring structure on K-theory of a quotient of the Fermat quintic

  39. A refined comparison of isomorphic vector bundles on a compact space

  40. fibrations of classifying spaces - Leray Hirsch Theorem converse
  41. Looking for generalization of projective model structure
  42. Finding decomposition of Steenrod operators?

  43. Two-to-one continuous mapping from R² to R²
  44. Relating two different approaches to the Atiyah-Hirzebruch Spectral Sequence
  45. Has anyone seen a nice map of multiplicative cohomology theories?

  46. Is there a "simplification" functor in algebraic topology?

  47. Relative Steenrod's problem
  48. Cohomology rings of $ GL_n(C)$, $SL_n(C)$
  49. Homotopy fiber of a map between classifying spaces

  50. Conditions for the second homotopy group to be Abelian

  51. Eilenberg-Steenrod Axioms for Lawson Homology

  52. Relations between Betti numbers for clique complex
  53. Homotopy type of the semi-simplicial set of symmetric groups
  54. Why is any $G$-resolution a principal $G$-bundle?
  55. Vector fields on quasi-spheres

  56. spectral sequence for a complex with two filtrations

  57. Obstruction to a general S^1-action

  58. Fiber homotopy equivalence

  59. Homotopy cosheaf?

  60. Does $\mathbb C\mathbb P^\infty$ have a group structure?

  61. Are infinite simplicial complexes all manifolds?

  62. Homotopy equivalence between two basepoints of the etale homotopy type of the one-torus

  63. Calculating topological index
  64. If $X$ and $Y$ are homotopy equivalent, then are $X \times \mathbb{R}^{\infty}$ and $Y \times \mathbb{R}^{\infty}$ homeomorphic?

  65. A property of slant product in group cohomology

  66. Cofree conilpotent (cocommutative) coalgebra for $\infty$-categories
  67. Is there a Whitney's approximation theorem for applications of pairs?
  68. When does homology represent an embedded sphere?

  69. $H^4(BG,\mathbb Z)$ torsion free for $G$ a connected Lie group
  70. Cohomology of $BE_8$ and $BSU(2)$

  71. How to prove that $\phi: \;\mathrm Mod(S_g)\to \mathrm Sp(2g, \mathbb{Z})$ is an epimorphism?

  72. Simply connected homology cobordisms
  73. Is Mac Lane still the best place to learn category theory?
  74. Non existence of commutative singular cochains vs quasi iso between cochains on BT and its cohomology
  75. Relation between the Hochschild cohomology of group algebras and groupoids

  76. A group of type F that is an extension of type F-by-type F
  77. Retracting a wedge of spheres off a homotopy fiber

  78. Non-zero homotopy/homology in diffeomorphism groups

  79. How does one introduce characteristic classes
  80. Integrating matrix maps

  81. Smooth classifying spaces?

  82. String Orientation and Level Structures

  83. Holes of a compact set in $\mathbb{R}^n$ that do not contain holes of a larger open set

  84. Relative de rham cohomology with compact support
  85. Stratification of space of labelled circles in the plane
  86. Criterion for alternation of the linking form
  87. Cofiber of the inclusion of an $E_0$-algebra $M$ into the free $E_k$-algebra generated by it

  88. Constructing ($\infty, 1)$-category from Morse theory on a manifold

  89. Long exact sequence of Quillen derived functors

  90. How much is known about unstable homotopy of truncated projective spaces? - Reference request
  91. Relation between the category of orthogonal G-spectra and the category of orthogonal H-spectra

  92. Recovering SU(2)-space when the orbit space is a 3 sphere with 3 singular orbits

  93. Is $\mathbb R^3$ the square of some topological space?
  94. "Strict" homotopy theory of topological stacks/orbifolds

  95. Cohomology of a homotopy pullback of groupoids

  96. Atiyah Bott-Shapiro orientation Vs Anderson-Brown-Peterson Splitting

  97. What can be said about the topological K-theory of non-singular varieties of small codimension in projective space?

  98. CW-complex of Eilenberg-MacLane spaces

  99. Homotopy limits commute with right Quillen functors
  100. Growth of stable homotopy groups of spheres