Pith Number

pith:AJOKH4S2

pith:2020:AJOKH4S2JSQJGXC33AW6LOWJA3

not attested not anchored not stored refs pending

The Geometry of Loop Spaces III: Isometry Groups of Contact Manifolds

Satoshi Egi, Steven Rosenberg, Yoshiaki Maeda

Wodzicki-Chern-Simons forms on the loop space of a circle bundle detect that the isometry group has infinite fundamental group for large Chern class.

arxiv:2011.01800 v9 · 2020-11-03 · math.DG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AJOKH4S2JSQJGXC33AW6LOWJA3}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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 use Wodzicki-Chern-Simons forms on the loop space LM_p to prove that π₁(Isom(M_p,g)) is infinite for |p| ≫ 0. We also give the first high dimensional examples of nonvanishing Wodzicki-Pontryagin forms.

C2weakest assumption

Existence of a metric g on M_p that is simultaneously compatible with the symplectic structure on the base and with the geometry of the circle fiber, so that the Wodzicki forms on LM_p are well-defined and detect non-trivial isometries (abstract, first paragraph).

C3one line summary

Proves π₁(Isom(M_p,g)) infinite for |p|≫0 in certain contact (4n+1)-manifolds via Wodzicki-Chern-Simons forms on LM_p, plus first high-dim nonvanishing Wodzicki-Pontryagin forms.

Receipt and verification

First computed	2026-06-02T01:03:27.543564Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

025ca3f25a4ca0935c5bd82de5bac906f8fa8a0fe87de58a8db4b36ba2782a80

Aliases

arxiv: 2011.01800 · arxiv_version: 2011.01800v9 · doi: 10.48550/arxiv.2011.01800 · pith_short_12: AJOKH4S2JSQJ · pith_short_16: AJOKH4S2JSQJGXC3 · pith_short_8: AJOKH4S2

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/AJOKH4S2JSQJGXC33AW6LOWJA3 \
  | 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: 025ca3f25a4ca0935c5bd82de5bac906f8fa8a0fe87de58a8db4b36ba2782a80

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d800febc102d32241554ae1e4af2e2ac84969319d089a22f0aa6769936dd8c6d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2020-11-03T15:48:05Z",
    "title_canon_sha256": "d3c3b76689bc99a7cf5999e1a45d72e5d0757244e94a637c1708ad35ecdbb146"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2011.01800",
    "kind": "arxiv",
    "version": 9
  }
}