Pith Number

pith:7CCHUZVT

pith:2026:7CCHUZVT4CM2N22NB6V2WAQE43

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Non-vanishing of homotopy groups of Manin--Schechtman arrangements

So Yamagata, Takuya Saito

Manin-Schechtman arrangement complements have non-vanishing higher homotopy groups and fail to be K(π,1) spaces in many cases.

arxiv:2605.14536 v1 · 2026-05-14 · math.AT · math.AG · math.CO

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Record completeness

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Claims

C1strongest claim

We study Manin--Schechtman arrangements... and prove that their complements have non-vanishing higher homotopy groups. Consequently, these arrangements fail to be K(π,1) in a broad range of cases.

C2weakest assumption

The proof relies on the specific combinatorial and geometric properties of the Manin-Schechtman arrangements as higher-dimensional analogs of the braid arrangement; if these properties do not hold or if the homotopy computation contains an undetected gap, the non-vanishing claim fails.

C3one line summary

Complements of Manin-Schechtman arrangements have non-vanishing higher homotopy groups and are therefore not K(π,1) spaces in a broad range of cases.

References

39 extracted · 39 resolved · 0 Pith anchors

[1] Agostini, Daniele and Brysiewicz, Taylor and Fevola, Claudia and K\"uhne, Lukas and Sturmfels, Bernd and Telen, Simon , TITLE =. Adv. Math. , FJOURNAL =. 2023 , PAGES =. doi:10.1016/j.aim.2023.108863 2023 · doi:10.1016/j.aim.2023.108863

[2] Athanasiadis, Christos A. , fjournal =. The largest intersection lattice of a discriminantal arrangement , volume =. Beitr\"age Algebra Geom. , mrclass =

[3] and Brandt, Keith A

[4] Bessis, David , TITLE =. Ann. of Math. (2) , FJOURNAL =. 2015 , NUMBER =. doi:10.4007/annals.2015.181.3.1 , URL = 2015 · doi:10.4007/annals.2015.181.3.1

[5] orner, Anders and Las Vergnas, Michel and Sturmfels, Bernd and White, Neil and Ziegler, G\

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:05.884464Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f8847a66b3e099a6eb4d0fabab0204e6edd9ae0e419ad6b0031b3f7995bc9132

Aliases

arxiv: 2605.14536 · arxiv_version: 2605.14536v1 · doi: 10.48550/arxiv.2605.14536 · pith_short_12: 7CCHUZVT4CM2 · pith_short_16: 7CCHUZVT4CM2N22N · pith_short_8: 7CCHUZVT

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7CCHUZVT4CM2N22NB6V2WAQE43 \
  | 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: f8847a66b3e099a6eb4d0fabab0204e6edd9ae0e419ad6b0031b3f7995bc9132

Canonical record JSON

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    "abstract_canon_sha256": "023fd7130449597c330471962c59dbfa1e9f70be3acf8ea06de1195065bdb069",
    "cross_cats_sorted": [
      "math.AG",
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2026-05-14T08:19:26Z",
    "title_canon_sha256": "74d226210d031b5b7a556844007d536e1a5292a3c0a2d4260a2ea7cacf5a5b92"
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  "source": {
    "id": "2605.14536",
    "kind": "arxiv",
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  }
}