Pith Number

pith:FZMSSHM5

pith:2026:FZMSSHM5QXOTFAVCUEO4274OXZ

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Rigidity of self-maps of $V_{n,2}$ and manifolds tangentially homotopy equivalent to $V_{n,2} \times S^k$

Sagnik Biswas

For most n, self-maps of the Stiefel manifold V_{n,2} homotopic to almost diffeomorphisms are determined, and manifolds tangentially homotopy equivalent to V_{n,2} × S^k are classified up to almost diffeomorphism for k=3,5 or 7 to n-3 (k ≠

arxiv:2604.15984 v2 · 2026-04-17 · math.AT · math.GT

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\pithnumber{FZMSSHM5QXOTFAVCUEO4274OXZ}

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4 Citations open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We determine, for most values of n, all self-maps of V_{n,2} that are homotopic to an almost diffeomorphism. We classify smooth closed manifolds tangentially homotopy equivalent to V_{n,2} × S^k up to almost diffeomorphism, for k = 3, 5 or 7 ≤ k ≤ n-3, k ≠ 2^i - 2.

C2weakest assumption

That explicit inverses in the structure set can be found via normal invariants of specific tangential homotopy equivalences under the stated conditions on k and n, without additional obstructions arising in the general case.

C3one line summary

Rigidity results for self-maps of V_{n,2} and classification of tangentially homotopy equivalent manifolds to V_{n,2} x S^k up to almost diffeomorphism for certain k.

Receipt and verification

First computed	2026-06-11T02:09:29.342703Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e59291d9d85dd3282a2a11dcd7f8ebe5b11cdd68374ecf267e0fee2bde1330e

Aliases

arxiv: 2604.15984 · arxiv_version: 2604.15984v2 · doi: 10.48550/arxiv.2604.15984 · pith_short_12: FZMSSHM5QXOT · pith_short_16: FZMSSHM5QXOTFAVC · pith_short_8: FZMSSHM5

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FZMSSHM5QXOTFAVCUEO4274OXZ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 2e59291d9d85dd3282a2a11dcd7f8ebe5b11cdd68374ecf267e0fee2bde1330e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "87ffd1c7f9f45fb018959ffe706678717acc3415282031ccd3bee7bb9da8c7cd",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2026-04-17T12:00:46Z",
    "title_canon_sha256": "d8471dd70b7e6531c384d806121fc1af155382d40bf6f39d280b91fb62cda8b9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.15984",
    "kind": "arxiv",
    "version": 2
  }
}